U.S. patent application number 12/192434 was filed with the patent office on 2008-12-25 for value-instance-connectivity computer-implemented database.
Invention is credited to Stephan A. TARIN.
Application Number | 20080319939 12/192434 |
Document ID | / |
Family ID | 22342004 |
Filed Date | 2008-12-25 |
United States Patent
Application |
20080319939 |
Kind Code |
A1 |
TARIN; Stephan A. |
December 25, 2008 |
VALUE-INSTANCE-CONNECTIVITY COMPUTER-IMPLEMENTED DATABASE
Abstract
A computer-implemented database and method providing an
efficient, ordered reduced space representation of
multi-dimensional data. The data values for each attribute are
stored in a manner that provides an advantage in, for example,
space usage and/or speed of access, such as in condensed form
and/or sort order. Instances of each data value for an attribute
are identified by instance elements, each of which is associated
with one data value. Connectivity information is provided for each
instance element that uniquely associates each instance element
with a specific instance of a data value for another attribute.
Inventors: |
TARIN; Stephan A.; (New
York, NY) |
Correspondence
Address: |
JONES DAY
222 EAST 41ST ST
NEW YORK
NY
10017
US
|
Family ID: |
22342004 |
Appl. No.: |
12/192434 |
Filed: |
August 15, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10629812 |
Jul 28, 2003 |
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12192434 |
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09412158 |
Oct 5, 1999 |
6606638 |
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10629812 |
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09112078 |
Jul 8, 1998 |
6009432 |
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09412158 |
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Current U.S.
Class: |
1/1 ;
707/999.001; 707/E17.009 |
Current CPC
Class: |
Y10S 707/99934 20130101;
Y10S 707/99933 20130101; G06F 16/283 20190101; Y10S 707/99944
20130101; G06F 16/22 20190101; Y10S 707/99932 20130101; Y10S
707/99943 20130101 |
Class at
Publication: |
707/1 ;
707/E17.009 |
International
Class: |
G06F 17/30 20060101
G06F017/30 |
Claims
1. A method of retrieving a record from a compressed database: a.
retrieving information regarding the number of occurrences of a
given value from the database, the database having been compressed
by storing information regarding distinct values of an attribute
and information regarding the number of occurrences of distinct
values; b. determining an instance element based on information
regarding the number of occurrences of the given value; c.
determining a connectivity element based on the instance element;
and d. determining a record from the connectivity element.
2. The method of claim 1, wherein the step of retrieving the
information regarding the number of occurrences of the given value
comprises analyzing a cardinality store.
3. The method of claim 1, wherein the step of determining an
instance element information regarding the number of occurrences of
the given value comprises analyzing an instance store.
4. The method of claim 1, wherein the step of determining the
connectivity element comprises analyzing a connectivity store.
5. The method of claim 1, wherein the step of determining a record
comprises analyzing a value store.
6. The method of claim 1, wherein the retrieving of the record is
caused by an Structured Query Language (SQL) query.
7. The method of claim 1, wherein the SQL query is a SELECT query.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of application Ser. No.
10/629,812 filed on Jul. 28, 2003, which is a division of
application Ser. No. 09/412,158 filed on Oct. 15, 1999, now issued
as U.S. Pat. No. 6,606,638, which is a continuation of application
Ser. No. 09/112,078 filed on Jul. 8, 1998, now issued as U.S. Pat.
No. 6,009,432.
FIELD OF INVENTION
[0002] The present invention relates generally to
computer-implemented databases and, in particular, to an efficient,
ordered, reduced-space representation of multi-dimensional
data.
BACKGROUND OF THE INVENTION
[0003] State of the art database management systems (DBMS's), like
the underlying data files out of which and on top of which they
historically grew, continue to store and manipulate data in a
manner that closely mirrors the users' view of the data. Users
typically think of data as a sequence of records (or "tuples"),
each logically composed of a fixed number of "fields" (or
"attributes") that contain specific content about the entity
described by that record. This view is naturally represented by a
logical table (or "relation") structure (referred to herein as a
"record-based table"), such as a rectilinear grid, in which the
rows represent records and the columns represent fields.
[0004] The long-standing existence of record-based tables and their
correspondence to a conventional user view, in the absence of
generally recognized drawbacks, has led to their nearly universal
acceptance as the major underlying internal representation of
databases. Yet record-based tables contain key structural
weaknesses including high levels of unorderedness and redundancy
that have traditionally been regarded as unavoidable. For example,
such tables can be sorted or grouped (i.e., the contiguous
positioning of identical values) on at most one criterion (based
upon column values or some function of either column values or
multiple column values). This limitation renders essential database
functions, such as querying and updating, on all criteria other
than this privileged one awkward and overly resource-intensive.
[0005] The above deficiencies inhere in the fundamental properties
of the record-based table structure, in particular, the requirement
that the positioning of each field be made co-linear with all other
fields in the same record. This arbitrary positioning of fields in
record-based table structures excludes all other arrangements. It
thus obscures natural and exploitable latent data relationships
that are revealed by more ordered, condensed and efficient data
arrangements. Moreover, the inability of record-based tables to
effectively group or sort data leads to negative characteristics of
state of the art DBMS's such as unorderedness, redundancy,
cumbersomeness, algorithmic inefficiencies and performance
instabilities.
[0006] Database research provides palliatives for these problems,
but fails to uncover and address their underlying cause (i.e., the
reliance on record-based table structures). For example, the
inability to represent a natural, multi-dimensional grouping within
the confines of a record-based table structure has led to the
creation of index-based data structures. These supplementary
structures are inherently and often massively redundant, but they
establish groupings and orderings that cannot be directly
represented using a conventional table. Index-based structures
typically grow to be overly lengthy, convoluted and are cumbersome
to maintain, optimize and especially update. Examples of common
indexes are b-trees, t-trees, star-indexes, and various bit
maps.
[0007] Other supplementary structures developed in the prior art
have different drawbacks. For example, hash tables can provide
rapid querying of individual data items, but their lack of sort
ordering render them unsuitable for range queries or for any other
operation that requires returning data in a specific order.
[0008] The ability to maintain an ordered, non-redundant,
multi-dimensional data set, using flexible sorting and/or grouping
criteria, is extremely useful to database management. Sorted data
makes rapid searching and updating possible via, for example,
binary search algorithms and insertion sorts. Grouped data enables
condensation that reduces space requirements and further increases
the speed of, for example, searching and updating.
[0009] A system of data storage in which most or all columns of a
data table can be stored in grouped and/or sorted order is thus
extremely desirable. Previous studies have investigated "fully
inverted databases," which index each column through traditional
methods, preserving all the inadequacies of records and indexes.
Additionally, the bloated storage requirements necessary to
accommodate complete indexing tend to make fully inverted databases
impractical, especially, but not only, in main memory
databases.
SUMMARY OF THE INVENTION
[0010] It is therefore an object of the present invention to
provide a fully or partially ordered (e.g., grouped and/or sorted)
database without the deficiencies characteristic of the prior art,
as mentioned above.
[0011] Briefly, instead of structuring a database as a table in
which each row is a record and each column contains the fields in
the record, as in earlier databases, the present invention permutes
or otherwise modifies the columns to provide an advantage in, for
example, space usage and/or speed of access, such that the rows no
longer necessarily correspond to individual records. For example,
one such modification is to condense the column by eliminating
redundant values (which reduces memory usage); another is
sort-ordering the column, ensuring that value groups will always
appear in some particular order (which can greatly reduce the time
required to search a column for a particular value); still another
is to both condense and sort a column. Other permutations and
modifications with other advantages are also possible. The table of
permuted/modified values is referred to herein as the "value
table."
[0012] Logically, though not necessarily physically, separate data
structures provide the information needed to reconstruct the
"records" in the database. In particular, they provide "instance"
and "connectivity" information, where instance information
identifies the instances of each value in the field that is in a
record and connectivity information associates each instance with a
specific instance of a value in at least one other field.
[0013] In one embodiment of the invention, both the instance and
connectivity information is provided in a table, referred to herein
as the "instance table." Each column in the instance table
corresponds to an attribute of the records in the database and is
associated with a column in the value table that contains the
values for that attribute (and possibly other attributes). Each
cell (row/column location) in the instance table has a position (in
one embodiment of the invention, its row number) and an instance
value (the contents of the cell). An associated cell in the
associated column of the value table is derived from each instance
cell's position. Also, an associated instance cell in another
column of the instance table that belongs to the same record is
derived from each instance cell's instance value. Thus, in this
embodiment, an instance cell's position identifies the value which
the cell is an instance of and an instance cell's contents provides
the connectivity information associating the instance with another
instance cell in another field. A record can then be reconstructed
starting at a cell in the instance table by deriving, from the
cell's position, the associated value cell in the value table and,
from the cell's instance value, the position of the associated
instance cell, and repeating this process at the associated
instance cell and so forth, with a last cell in the chain
providing, in one embodiment, the corresponding position of the
starting cell.
[0014] If a column of the value table is sorted but not condensed,
the value table column and the associated column in the instance
table has, in one embodiment of the invention, the same number of
rows. An instance cell's associated value cell is, in this one
embodiment, the value cell in the associated value table column
having the same row number as the instance cell. An instance cell's
associated instance cell (i.e., cell in another column of the
instance table belonging to the same record) is the cell in a
specified column having the row number given by the instance cell's
instance value. In one embodiment, the specified column is the next
column in the instance table with the last column referring back to
the first column. For example, if column 1 of the value table is
uncondensed and, after permutation, column 1, row 2 and column 2,
row 5 of the value table belong to the same record and an instance
of column 2, row 5 is at column 2, row 5 of the instance table, the
instance table at column 1, row 2 would contain the number 5
(indicating that row 5 of the next column belongs to the same
record).
[0015] If a value table column is condensed, there is in general no
longer a one-to-one correspondence between that column and an
instance table column that is associated with it. In this case, a
table, referred to herein as a "displacement table," is provided
that, in one embodiment of the invention, has a column for each
instance table column associated with a condensed value table
column and specifies the range of instance table row numbers
associated with each row of the value table column. The value cell
associated with an instance cell is then determined by the
corresponding displacement table column based on the instance
cell's position (row number). In one embodiment, a displacement
table column has the same number of rows as an associated value
table column with each cell in the displacement table providing the
first row number in the range of instance table row numbers
associated with the corresponding value cell. Alternatively, each
cell in the displacement table could, for example, provide the last
row number in the range of instance table row numbers, the total
number of rows in the range, or some other value from which it is
possible to derive the range of instance table row numbers
associated with each value cell (i.e., the instances of each
value).
[0016] One drawback of the displacement table, as just described,
is that searching the displacement table for the value cell
corresponding to an instance cell slows record reconstruction. This
drawback is addressed in still another embodiment of the invention
in which the instance value of an instance cell whose associated
instance cell is in a column having a displacement column is set to
the position of the value cell associated with the associated
instance cell (as opposed to the position of the associated
instance cell itself, as in the embodiment described above). The
value of the associated instance cell is then directly obtainable
without a search of the displacement table. In this embodiment, a
table, referred to herein as an "occurrence table," provides
information for determining the associated instance cell.
[0017] In one embodiment of the occurrence table, each column in
the instance table that has cells with instance values as just
described has an associated column in the occurrence table that has
the same number of rows. A cell in the occurrence table is
associated with a cell in the instance table based, in this
embodiment, on its position and specifies an offset. The offset is
added to the first row number in the range of instance table row
numbers associated with the value cell to arrive at the associated
instance cell. The first row number is derived from the
displacement table based on the instance value of the instance
cell. The connectivity information for an instance cell is thus
provided in this embodiment by the instance cell's contents, the
occurrence table and the displacement table.
[0018] The data structures described herein may be, but need not
be, entirely in RAM or distributed across a network comprised of a
multiplicity of data processors. They may also be implemented in a
variety of ways and the invention herein is in no way limited to
the examples given of particular implementations. For example one
embodiment may involve only partly storing the data set using the
computer-implemented database and methods described herein, with
the remainder stored using traditional table-based methods.
Information may be stored in various formats and the invention is
not limited to any particular format. The contents of particular
columns may be represented by functions or by functions in
combination with other stored information or by stored information
in any form, including bitmaps.
[0019] More generally, while the value, instance, displacement and
occurrence tables have been described as "tables" having rows,
columns and cells, the invention is not limited to such structures.
Any computerized data structure for storing the information in
these tables may be used. For example, the value table described
above is a specific example of a "value store" (i.e., it stores the
data values representing the user-view values of information in the
database); the instance table is a specific example of an "instance
store" and a "connectivity store" (i.e., it both identifies
instances of data items in the value store and represents
relationships among instances of data items in the value store);
and the displacement table is a specific example of a "cardinality
store" (i.e., it represents the frequency of occurrence of equal
instances of data values). The columns of a table are specific
examples of a "list" or, more generally, a "set." A "set," for the
purposes of the present invention, comprises one or more
"elements," each having a value or values and a "position," where
the position specifies the location of the element within the set.
In the discussion above, a "cell" in a column of a table is an
example of an "element" and its position in the set is its row
number.
[0020] Furthermore, although the embodiments described herein refer
to and manipulate traditional "records", the invention is not
limited to records and is generally applicable to represent
relationships between data values. All such variations are
alternate embodiments of this invention.
[0021] Typical database operations supported by the database system
of the present invention include, but are not limited to:
[0022] 1) reconstructing physical records,
[0023] 2) finding records matching query criteria,
[0024] 3) joining tables in standard ways,
[0025] 4) deleting and/or adding records,
[0026] 5) modifying existing records, and
[0027] 6) combinations of these and other standard database
operations to perform useful tasks.
[0028] The present invention provides a new and efficient way of
structuring databases enabling efficient query and update
processing, reduced database storage requirements, and simplified
database organization and maintenance. Rather than achieve
orderedness through increasing redundancy (i.e., superimposing an
ordered data representation on top of the original unordered
representation of the same data), the present invention eliminates
redundancy on a fundamental level. This reduces storage
requirements, in turn enabling more data to be concurrently stored
in RAM (enhancing application performance and reducing hardware
costs) and speeds up transmission of databases across communication
networks, making high-speed main-memory databases practical for a
wide spectrum of business and scientific applications. Fast query
processing is possible without the overhead found in a fully
inverted database (such as excessive memory usage). Furthermore,
with the data structures of the present invention, data is much
more easily manipulated than in traditional databases, often
requiring only that certain entries in the instance table be
changed, with no copying of data. Database operations in general
are thus more efficient using the present invention. In addition,
certain operations such as histographic analysis, data compression,
and multiple orderings, which are computationally intensive in
record-oriented structures, are obtainable immediately from the
structures described herein. The invention also provides improved
processing in parallel computing environments.
[0029] The database system of the present invention can be used as
a back-end for an efficient database compatible with almost any
database front-end employing industry standard middleware (e.g.,
Microsoft's Open Database Connectivity (ODBC) or Microsoft's
Active-X Data Objects (ADO)) and will provide almost drop-in
compatibility with the large corpus of existing database software.
Alternatively, a native stand-alone engine can be directly
implemented, via, for example, C++ functions, templates and/or
class libraries. Implemented either as a back-end to middleware or
as a stand-alone engine, this invention provides a database that
looks familiar to the user, but which is managed internally in a
novel and efficient manner.
BRIEF DESCRIPTION OF THE DRAWINGS
[0030] FIG. 1 is a block diagram of one embodiment of the present
invention.
[0031] FIG. 2 illustrates a simple ring topology.
[0032] FIG. 3 illustrates a topology having subrings with a bridge
field.
[0033] FIG. 4 illustrates a "star" topology.
[0034] FIG. 5 is a flowchart illustrating a routine that finds the
value table cell associated with an instance table cell.
[0035] FIG. 6 illustrates a routine that determines the row of the
next column where the current column is V/O split.
[0036] FIG. 7 is a flowchart illustrating the mapping of a record's
topology data into a linear array.
[0037] FIG. 8 is a flowchart illustrating the process of writing a
linearized record topology into an instance table.
[0038] FIG. 9 is a flowchart illustrating the interchange of the
cells of two records in the instance table.
[0039] FIG. 10 is a flowchart illustrating swapping a live for a
deleted cell.
[0040] FIG. 11 is a flowchart illustrating finding the undeleted
cell (if any) immediately adjoining the deleted cell(s) (if any)
for a given value's instance cells in the instance table.
[0041] FIG. 12 is a flowchart illustrating moving a free (deleted
instance) cell in the instance table from its original associated
value to the immediately preceding value.
[0042] FIG. 13 is a flowchart illustrating moving a free (deleted
instance) cell in the instance table from its original associated
value to the immediately following value.
[0043] FIG. 14 is a flowchart illustrating determining the total
number of instances (including deleted instances) for a given
value.
[0044] FIG. 15 is a flowchart illustrating the deletion of a
previously live instance cell in the instance table.
[0045] FIG. 16 is a flowchart illustrating the insertion of a new
value into a value table column, when the pointers into that column
are not V/O split.
[0046] FIG. 17 is a flowchart illustrating the insertion of a new
value into a value table column, when the pointers into that column
are V/O split.
[0047] FIG. 18 is a flowchart illustrating the assignment of a free
(deleted) instance table cell to a given value in the value
table.
[0048] FIG. 19 is a block diagram illustrating the steps in a
delete record operation.
[0049] FIG. 20 is a block diagram illustrating the steps in an add
record operation.
[0050] FIG. 21 is a block diagram illustrating the steps in a
modify record operation.
[0051] FIG. 22 is a block diagram illustrating the steps in a query
operation.
[0052] FIG. 23 is a block diagram illustrating the steps in a join
operation.
DETAILED DESCRIPTION
[0053] FIG. 1 illustrates the basic hardware setup of an embodiment
of the present invention. Program store 4 is a storage device, such
as a hard disk, containing the software that performs the functions
of the database system of the present invention. This software
includes, for example, the routines for generating the data
structures of the underlying database and for reformatting legacy
databases, such as those in record-oriented files, into those data
structures. In addition, the software includes the routines for
manipulating and accessing the database, such as query, delete,
add, modify and join routines. Data files are stored in storage
device 2 and contain the data associated with one or more
databases. Data files may be formatted as binary images of the data
structures herein or as record-oriented files. Program store 4 and
storage device 2 may be different parts of a single storage device.
The software in program store 4 is executed by processor 5, having
random access memory (RAM) 7. The selection of the tasks to be
performed by the database system is determined by a user at user
station 6.
[0054] In the following discussion, the term "pointer" is used in a
general sense to include both the C/C++ language meaning (a
variable containing a memory address) and, more generally, any data
type which is used to uniquely describe a location in storage,
whether that storage be RAM, disk, etc. A pointer implemented as an
integer offset from the beginning of a given data structure will
perform the same function as a C/C++ pointer while advantageously
requiring less storage. The terms memory and storage, used herein,
mean any electronic, optical or other means of storing data. The
term multi-dimensional is used herein in a mathematical or
quasi-mathematical sense to refer to a view of the data in which an
n-column record-based table is considered to occupy an
n-dimensional vector space. It is not used in its narrower sense,
sometimes used in data warehousing and On-Line Analytical
Processing (OLAP), where multi-dimensionality refers to multiple
layers of data analysis.
Basic Database Structure
[0055] Record-based tables, in which each row represents a record
and each column is a field in the record, are commonly used in
state of the art databases. A database in accordance with the
present invention differs from this known structure. In one
embodiment, the database is divided into two basic data structures;
an uncondensed value table and an instance table. The value table
contains the same data instances as prior art databases, but each
column may be permuted or otherwise changed and thus a row no
longer necessarily corresponds to a particular record. In
accordance with this embodiment, the instance table provides the
means for reconstructing the records from the value table.
Specifically, in one embodiment, the instance table has the same
number of rows and columns as the uncondensed value table and each
cell (i.e., row/column location) in the instance table contains the
row number for the next field in the same record ("next" being
defined below). Thus, the value of the next field of the record
containing Value_Table(r, c), where r and c are the row and column
of a particular location in the value table, is
Value_Table(Instance_Table(r, c), next(c)), where Instance_Table(r,
c) is the row number of the next field. The function next(c)
obtains the next column from the current one. In one embodiment of
the present invention using a ring topology, next(c)=((c+1) mod n),
where n is the number of columns and the columns are numbered from
0 to n-1 (zero-based indexing). In an alternate embodiment (columns
numbered 1 to n), next(c)=c mod n+1. A wide variety of topologies
are possible, each having a corresponding next(c) function.
[0056] For example, below is a database in the standard
one-record-per-row format, with 1-based row numbering:
[0057] Prior Art Database
TABLE-US-00001 ENGLISH SPANISH GERMAN TYPE PARITY Record # (col. 0)
(col. 1) (col. 3) (col. 4) (col. 5) 1 One Uno Eins Unit Odd 2 Two
Dos Zwei Prime Even 3 Three Tres Drei Prime Odd 4 Four Cuatro Vier
Power2 Even 5 Five Cinco Fuenf Prime Odd 6 Six Ses Sechs Composi
Even
[0058] The corresponding value and instance tables arranged in
accordance with a specific embodiment of the present invention
are:
[0059] Value Table:
TABLE-US-00002 ENGLISH SPANISH GERMAN TYPE PARITY Row # (col. 0)
(col. 1) (col. 2) (col. 3) (col. 4) 1 Five.sup.5 Cinco.sup.5
Drei.sup.3 Compos.sup.6 Even.sup.2 2 Four.sup.4 Cuatro.sup.4
Eins.sup.1 Power2.sup.4 Even.sup.4 3 One.sup.1 Dos.sup.2
Fuenf.sup.5 Prime.sup.2 Even.sup.6 4 Six.sup.6 Ses.sup.6
Sechs.sup.6 Prime.sup.3 Odd.sup.1 5 Three.sup.3 Tres.sup.3
Vier.sup.4 Prime.sup.5 Odd.sup.3 6 Two.sup.2 Uno.sup.1 Zwei.sup.2
Unit.sup.1 Odd.sup.5
[0060] Instance Table:
TABLE-US-00003 ENGLISH SPANISH GERMAN TYPE PARITY Row # (col. 0)
(col. 1) (col. 2) (col. 3) (col. 4) 1 1 3 4 3 6 2 2 5 6 2 2 3 6 6 5
1 4 4 4 4 1 5 3 5 5 1 2 6 5 6 3 2 3 4 1
[0061] The value table shown above is created by sorting each
column, in this case, in alphabetical order. For explanatory
purposes only, a superscript has been placed next to each value to
indicate its record number in the original database.
[0062] After sorting the columns, a row of the value table will not
generally correspond to a single record in the original database.
The instance table however provides the information necessary to
reconstruct those records to the traditional external record view.
Specifically, each cell (i.e., row/column location) in the instance
table is associated, in the above embodiment, with a single record.
The cell with the same row/column location in the value table
contains the value of the record for the field associated with the
column. The instance table cell itself contains the row number of
the next field of the record.
[0063] For example, suppose the record containing row 1 of the
"English" column (column 0) of the instance table is to be
reconstructed. The associated cell in the value table (i.e., row 1,
column 0) contains the value "Five". Taking the other fields (or
columns) in order, first the row of the "Spanish" column (column 1)
belonging to the same record as row 1 of the "English" column
(column 0) is determined. The information is provided by the
instance table at row 1/column 0, which in this case contains the
number 1, meaning row "1" of the Spanish column is in the same
record as row "1" of the English column. Next, to determine the row
of the "German" column (column 2) from the same record as row "1"
of the Spanish column (column 1), row 1/column 1 in the instance
table is read, which contains the number 3, meaning row "3" of the
"German" column is from the same record. Tracing this record
through, row 3 of the "German" column (column 2) in the instance
table provides the row of the "Type" column (column 3) in the same
record and it contains the number 5--meaning row "5" of the "Type"
column is from the same record as row 3 of the "German" column. Row
5 of the "Type" column (column 3) indicates that the corresponding
row in the "Parity" column (column 4) is row 6. Finally, row 6 of
the "Parity" column (column 4) in the instance table, which is the
last column in the table, indicates that the corresponding row from
the "English" column, the first column in the table (column 0), is
row 1, which is where the process started. This is due to the ring
topology used in this example.
[0064] Thus, in accordance with the embodiment illustrated above,
each row/column location in the instance table contains the row
number in the next column which belongs to the same record, with
the last column containing the row number of the same record in the
first column. The links between the row/column locations belonging
to the same record would, in this embodiment, form a ring through
the instance table, as illustrated in FIG. 2. As this ring is
traversed, directly corresponding row/column locations in the value
table allow recovery of each field's value. Topologies other than a
ring may be used in alternate embodiments of the present
invention.
Generation of Value and Instance Tables from Record-Oriented
Data
[0065] Value and instance tables can be generated in accordance
with the present invention using the data in a prior art
record-oriented database format.
[0066] First, the value table is created by permuting or otherwise
changing the data in each column of the original database. Examples
of changes in a value table column are sort ordering the data and
grouping like values together. Different columns may be permuted or
changed differently. A sort order should be chosen based on its
usefulness for display or retrieval purposes in actual
applications. The requirement for a potential sort order is that it
have a computable predicate which orders the values. Some columns
may remain unsorted. In the example above, all columns were sorted
in alphabetic order.
[0067] In one embodiment, during this first step, a temporary
intermediate table is created that facilitates generation of the
instance table in the second step below. The intermediate table, in
this embodiment, has rows that correspond to records, as in the
original prior art database, and columns that indicate the permuted
position of the corresponding field in the value table. The
intermediate table for the above example (in which the permutations
are sort orderings) is as follows:
[0068] Intermediate Table:
TABLE-US-00004 ENGLISH SPANISH GERMAN TYPE PARITY Record # (col. 0)
(col. 1) (col. 2) (col. 3) (col. 4) 1 3 6 2 6 4 2 6 3 6 3 1 3 5 5 1
4 5 4 2 2 5 2 2 5 1 1 3 5 6 6 4 4 4 1 3
[0069] Thus, for example, the intermediate table indicates that the
"English" field for the original record 5 is in row 1 of the value
table, the "Spanish" field for record 5 is in row 1 of the value
table, the "German" field for record 5 is in row 3 of the value
table, the "Type" field for record 5 is in row 5 of the value table
and the "Parity" field for record 5 is in row 6 of the value
table.
[0070] In accordance with this embodiment, the instance table is
then determined as follows:
[0071] Instance_Table(Intermediate_Table(r, c),
c)=Intermediate_Table(r, next(c)),
[0072] for each row r and column c in the intermediate table and
where next(c) is defined above. In other words, each cell in the
intermediate table specifies a row of the corresponding column in
the instance table; that row in the instance table receives the
value in the next column of the intermediate table.
[0073] For example, referring to record number 5 in the example
above, the "English" field (column 0) in the intermediate table
contains the number 1 and the next field, "Spanish," (column 1)
also contains the number 1. Based on this information, the value 1
(i.e., the row number of the "Spanish" field of record 5 in the
sorted value table) is placed in row 1 of the instance table (i.e.,
the location of the "English" field of record 5 in the sorted value
table). Row 1 of the "Spanish" field in the instance table is set
to the value in the "German" field (column 2) of record number 5 in
the intermediate table (i.e., the value 3), which corresponds to
the row number of the "German" field in the sorted value table.
This process is repeated for each field, again with the last field
wrapping around to the first field.
[0074] A person skilled in the art will recognize that there are
equivalent algorithms, some possibly avoiding the use of an
intermediate table, for generating the instance table, and the
present invention is not limited to the algorithm shown here.
Condensed Value Table
[0075] In certain situations, the data in the value table may be
more efficiently represented in terms of space (e.g., memory or
disk usage) if certain columns are "condensed" by eliminating
redundant values. For example, in the value table above, the
"Parity" field has only two different values ("Even" and "Odd") and
the "Type" field has only four different values ("Compos",
"Power2", "Prime" and "Unit"). (The number of unique values for a
given field is called its "cardinality.") Accordingly, in a
preferred embodiment of the present invention, redundancy can be
eliminated by constructing a condensed value table, which for the
example above is as follows:
[0076] Condensed Value Table:
TABLE-US-00005 ENGLISH SPANISH GERMAN TYPE PARITY Row # (col. 0)
(col. 1) (col. 2) (col. 3) (col. 4) 1 Five Cinco Drei Composi Even
2 Four Cuatro Eins Power2 Odd 3 One Dos Fuenf Prime 4 Six Ses Sechs
Unit 5 Three Tres Vier 6 Two Uno Zwei
[0077] To realize this space savings, the storage for the value
table must be allocated in the appropriate manner; for example,
allocating each column as a separate vector or list, as opposed to
allocating the table as a two-dimensional array. In addition, the
changes applied to the columns should group equal values
together.
[0078] In order to retain the original information of the
uncondensed value table, an additional structure, referred to
herein as a "displacement" table, is provided in a preferred
embodiment. In one embodiment of the present invention, the
displacement table provides either the first or the last row number
at which each unique value in a column occurs in the original
uncondensed value table (referred to herein as "first row number"
and "last row number" format, respectively). For example, the
displacement table for the condensed value table above is as
follows (in "first row number" format):
[0079] Displacement Table:
TABLE-US-00006 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 (no
condensation, so no displacement 1 1 2 table columns for ENGLISH, 2
4 3 SPANISH, or GERMAN) 3 4 6 5 6
[0080] The "Parity" column of the displacement table thus indicates
that the value in the first row of the condensed value table (i.e.,
"Even") was in row 1 of the uncondensed value table (that is, the
value "Even" first appeared in row 1) and the value in the second
row of the condensed value table (i.e., "Odd") first appeared in
row 4 of the uncondensed value table. Alternatively, the record
counts for each value may be stored in the displacement table with
the first row for each value being arithmetically derived, or some
arithmetic combination of the count and displacement may be
used.
[0081] A column having field width W bytes and cardinality C (i.e.,
C unique values) is represented by a "condensed" column of unique
values, together with a displacement table of integer values (row
numbers) of size P bytes in W*C+P*C bytes of RAM, whereas storage
of the uncondensed column requires W*N bytes (where N is the number
of records). Thus, where
W*C+P*C<W*N, or
C<N/(1+P/W),
[0082] this type of compression is beneficial.
[0083] The condensed columns in this embodiment generally destroys
the one-to-one correspondence between the cells (i.e., row/column
locations) of the instance table and the cells of the value table.
Thus, during record reconstruction, the value for a cell cannot be
retrieved when traversing the instance table simply by looking at
the value in the value table at the same row/column location. For
example, there is no longer a cell in the value table at the same
row/column location as column 3 ("Type"), row 5 of the instance
table in the example above.
[0084] Instead, in accordance with a preferred embodiment, the
value of the field associated with Instance_Table(r, c), where c is
a condensed column, is given by Value_Table(disp_row_num, c), where
disp_row_num is the row number of the cell in the displacement
table for the cth column for which
Displacement_Table(disp_row_num,c)<=r<Displacement_Table(disp_row_-
num+1,c),
[0085] where the upper-bound test is not performed if
disp_row_num+1 does not exist (i.e., if disp_row_num is the last
Displacement_Table row for column c) (for "first row number"
Displacement_Table format), or
Displacement_Table(disp_row_num1,c)<r<=Displacement_Table(disp_row-
_num,c)
[0086] where the lower-bound test is not performed if
disp_row_num-1 does not exist.
[0087] (for "last row number" Displacement_Table format).
[0088] Again referring to the example above, to find the value in
the value table associated with row 5 of column 3, the row in
column 3 of the displacement table that has the largest value not
greater than 5 is located. That is row 3 in the displacement table
above (row 4 having the value 6, which is greater than 5). Thus,
row 3 of column 3 has the value in the value table associated with
row 5 of column 3 in the instance table.
Space-Saving Techniques Applicable to Certain Types of Data
[0089] In accordance with a specific embodiment, fields with data
having certain properties can be incorporated into the database
system of the present invention without using some of the
structures described above (i.e., value, displacement and/or
instance tables). This is the case where the information that would
be contained in these structures is already present in the system
in an implicit form; i.e., the information is deducible from
characteristics of the data or other information that is present.
For example, if an uncondensed value table column contains the
numbers from 1 to N, there is no need to store this information in
the value table at all, because the information is implicitly in
the instance table (row 1 of the instance table corresponds to
value 1, and so forth). Each column (field) descriptor's
information states which structures are implicit for that field and
where and how to obtain the implicit data. In the example just
given, the column descriptor for the instance table column would
state that the value corresponding to each row is the row number.
This data can then be used in the algorithms described herein, or
other implementations of the algorithms.
[0090] When the special circumstances exist where "implicit"
structures can be used, space savings can be achieved. Examples of
such circumstances include, but are not limited to, the
following:
[0091] 1) A field having unique values requires no displacement
list since each value in the field's value list appears only once
in the instance list.
[0092] 2) A field having contiguous, unique, integer values that
have the same range as the rows of the value table requires no
value list and no displacement list. These values will sort so that
their value would be equal to their position in a value list, which
would also be their position in the instance list. Thus, their
value is equal to their position (row) in the instance list, so no
separate value list is needed. Since these values are unique, no
displacement list is needed either.
[0093] 3) A field having values that are the output values of a
function of contiguous integer input values requires no value list
if the function produces ordered outputs given ordered inputs (as
would be the case, for example, for a monotonic function). Values
are computed by applying the function to the position (row) of a
cell in the instance list. Since row positions are ordered
contiguous integers, the output of the function will also be
ordered. Thus no value list is needed since the values can be
computed from the instance list. Since the functions' output values
are always unique for unique inputs, no displacement list is
necessary either.
[0094] 4) A field having values that are approximated by the output
values of a function of contiguous integer input values can be
implemented with a reduced-spaced value list if the function
produces ordered outputs given ordered inputs (as would be the
case, for example, for a monotonic function). The value list in
this case need only contain the offset of the output of the
function, instead of the full value, and is arranged such that the
offsets plus the outputs of the function produce ordered
values.
[0095] 5) A sequence of contiguous instance list elements all
associated with the same data value and all having associated
(e.g., next) instance list elements associated with the same data
value can be represented by a single entry identifying, for
example, the associated data value, the position of the associated
instance element's associated data value and the number of instance
elements in the sequence, with the displacement list adjusted
appropriately.
[0096] Additionally, known compression and space-reduction
techniques may be applied to the value and instance tables (and
other structures). For example, values may be represented using
dictionary-type methods, including methods that match bit patterns
that are less than the entire length of a value. An effect of this
compression and the compression techniques above is to produce more
random bit patterns, which in turn improves hashing performance. In
addition, the value table, instance table and other structures may
be compressed, for example, using methods that take advantage of
repeated bit patterns, such as run-length encoding, and word
compaction (i.e., packing values into physical data storage units
when there is a mismatch between the value size and the physical
storage unit). The instance table can be further compressed, for
example, by reordering the relative positions of the columns and
the instances within columns, where allowable, to optimize
performance of the above compression techniques.
Alternative Instance Table with Condensed Value Table
[0097] The displacement table discussed above slows record
reconstruction because values from condensed columns can be
obtained only after searching the displacement table. An
alternative configuration used in another embodiment of the present
invention is to modify the instance table so that entries in a
column pointing into a condensed column point instead directly into
the value table. An additional table is then provided, referred to
herein as the "occurrence" table, that contains information by
which the row number of the next column in the instance table can
be calculated. The "occurrence" table contains the occurrence
number of the particular value pointed to by the corresponding cell
in the instance table. Specifically, in an embodiment in which the
displacement table is in "first row number" format, row numbers in
the instance table are 1 based, and the occurrence table is also 1
based, the instance table row number of the next field equals
Occurrence_Table(r,c)+Displacement_Table(Instance_Table(r,c),next(c))-1
[0098] Variants on this embodiment include, but are not limited to,
zero based row numbering in the various structures, and/or zero
based occurrence numbering in the occurrence table, and/or "last
row number" format for the displacement table entries. Such
variants affect the formula above for determining the instance
table row number of the next field. For example, for zero based row
numbering in the occurrence and instance tables, zero-based
occurrence numbering and "last row number" format in the
displacement table, the instance table row number of the next field
is:
[0099] for Instance_Table(r, c)=0, [0100] Occurrence_Table(r,
c)
[0101] and for Instance_Table(r, c)>0:
Occurrence_Table(r,c)+Displacement_Table(Instance_Table(r,c)1,next(c))+1
[0102] (because Displacement_Table(Instance_Table(r, c) 1, next(c))
is the last row number for the previous value). In all such
embodiments, the instance and occurrence tables could be merged
into one table having two-part elements.
[0103] In the above example, the TYPE column points into the PARITY
column of the instance table and the PARITY column in the value
table is condensed. In accordance with this alternative embodiment,
the instance and occurrence tables are as follows:
[0104] Alternative Instance Table:
TABLE-US-00007 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 1 3 4 1 6
2 2 5 6 1 2 3 6 6 5 1 4 4 4 4 1 2 3 5 5 1 2 2 5 6 3 2 3 2 1
[0105] Occurrence Table:
TABLE-US-00008 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 3 2 2 3 1
4 2 5 3 6 1
[0106] Thus, the TYPE column of the instance table now points
directly at the associated row in the value table of the PARITY
column. For example, the TYPE column at row 5 of the instance table
above contains 2, meaning that row 2 of the PARITY column in the
value table contains the PARITY value for the same record
associated with row 5 of the TYPE column. In this case, row 2 of
the PARITY column contains the value "Odd." The associated row of
the PARITY column in the instance table is the value in row 5 of
the TYPE column of the occurrence table plus the value in row 2 of
the PARITY column of the displacement table minus 1; which is 3+4-1
or 6.
[0107] The value, instance, displacement and occurrence tables have
been described above as separately stored tables. However, in
alternative embodiments, this need not be the case. For example,
the value and displacement tables elements can be stored
adjacently, and the instance and occurrence table elements can
likewise be stored adjacently, in those columns with condensed
value tables. This may reduce storage cache misses while retrieving
data rows from the database, and also reduce operand fetch time by
allowing the adjacent elements to share the same base storage
address.
Skewering, or Nested Ordering
[0108] For a given value and displacement table, there are many
possible instance and occurrence tables generating the same record
set. This is because, for a value having multiple occurrences, the
occurrences of the value may be assigned to the physical records
having that value in arbitrary order. In general, the product of
the factorials of the various values' multiplicities gives the
number of instance/occurrence tables which generate the same
physical record set. (There are thus 414,720
(3!*1!*3!*1!*2!*1!*2!*!*5!*2!*!*3!*2!*1!) different
instance/occurrence tables which generate the records of the
SPJ.sub.mod database given below.)
[0109] In a ring topology, there exists a unique
instance/occurrence representation that simultaneously stores N
multikey "lexical" orderings (where N is the number of attributes
in the database) with no more overhead than that required to store
the individual sorted columns (a characteristic referred to herein
as "skewering"). Each column C defines one such ordering such that
that column is taken as the most significant attribute in the key,
with next(C) as the next most significant attribute, etc., to
column prev(C) as the least significant attribute in the key (where
prev(c) is the previous column in the ring structure). The ordering
is referred to as "lexical" herein because it is the same type of
ordering used to sort words alphabetically, i.e., the words are
sorted on the first letter, then words with the same first letter
are sorted on the second letter and so forth.
[0110] Skewering is illustrated below starting with a prior art
table labelled SPJ.sub.mod (excerpted from C. J. Date, Introduction
to Database Systems, Sixth Edition, inside front cover (1995)):
[0111] SPJ.sub.mod:
TABLE-US-00009 Rec # S# P# J# QTY 0000 S2 P3 J2 200 0001 S2 P3 J5
600 0002 S2 P5 J2 100 0003 S3 P4 J2 500 0004 S5 P2 J2 200 0005 S5
P5 J5 500 0006 S5 P6 J2 200
[0112] The condensed value and displacement tables, in accordance
with the embodiments described above, for SPJ.sub.mod are:
[0113] Value Table:
TABLE-US-00010 Row # S# P# J# QTY 0000 S2 P2 J2 100 0001 S3 P3 J5
200 0002 S5 P4 500 0003 P5 600 0004 P6 0005 0006
[0114] Displacement Table:
TABLE-US-00011 Row # S# P# J# QTY 0000 0 0 0 0 0001 3 1 5 1 0002 4
3 4 0003 4 6 0004 6 0005 0006
[0115] Three alternative instance/occurrence tables are shown
below, each reproducing the physical record set of SPJ.sub.mod. The
instance and occurrence tables are shown as a single combined table
with entries of the form instance/occurrence.
[0116] Each value in the value table corresponds to a contiguous
block of cells in the instance/occurrence table, which is defined
by the displacement table entries for that value. These blocks have
been indicated by alternating highlights in the instance/occurrence
tables printed below.
[0117] Instance/Occurrence (version 1):
TABLE-US-00012 ##STR00001##
[0118] Instance/Occurrence (version 2):
TABLE-US-00013 ##STR00002##
[0119] Instance/Occurrence (version 3):
TABLE-US-00014 ##STR00003##
[0120] In version 3 the entries within each value block are in
sorted order based on their instance and occurrence. The N (here,
4) multikey orderings naturally defined by SPJ.sub.mod are:
[0121] (S#,P#,J#,QTY),
[0122] (P#,J#,QTY,S#),
[0123] (J#,QTY,S#,P#), and
[0124] (QTY,S#,P#,J#),
[0125] where the fields are ordered from left to right in
descending order of significance.
[0126] In a prior art record-type table structured database, in
order to reconstruct the records in any of these orders, there is a
space-time tradeoff. If the records are to be reproduced quickly,
and in linear time, four separate indices are required, specifying
the four different sort orders. To avoid this redundant use of
space, a time-consuming search is required each time the lexical
order used is changed.
[0127] The skewered instance/occurrence table eliminates this
tradeoff. Any of the natural lexical orders can be produced in
linear time. For example, to reproduce the order (P#,J#,QTY,S#),
the cells in column P# are processed top to bottom, reconstructing
the record corresponding to each such cell. These records will be
in the desired lexical order. To illustrate, the records
corresponding to cells 0000 through 0006 of column P# are as
follows:
[0128] cell 0000 of column P#->S5 P2 J2 200
[0129] cell 0001 of column P#->S2 P3 J2 200
[0130] cell 0002 of column P#->S2 P3 J5 600
[0131] cell 0003 of column P#->S3 P4 J2 500
[0132] cell 0004 of column P#->S2 P5 J2 100
[0133] cell 0005 of column P#->S5 P5 J5 500
[0134] cell 0006 of column P#->S5 P6 J2 200
[0135] Similarly, records may be reproduced in any of the N lexical
orders by proceeding linearly down through the cells of the most
significant column of that chosen lexical order.
[0136] If the columns of the value table are sorted and condensed,
as described earlier, a skewered instance/occurrence table is
formed by creating a multi-key lexical ordering starting at any
column. The other N-1 multi-key lexical orderings automatically
result.
Preserving Standard Database Formats Within the Database System of
the Present Invention
[0137] The present invention allows the option of maintaining
portions of a database in conventional form without incurring
significant additional overhead. This may be desired, for example,
for a column that cannot be compressed and will not be queried. An
illustrative embodiment is shown below.
[0138] For purposes of this illustration, a French column, which
will not be translated into the data structures of the present
invention, is added to the original prior art database as shown
below:
[0139] Prior Art Database:
TABLE-US-00015 Record ENG- SPAN- # LISH ISH GERMAN TYPE PARITY
FRENCH 1 One Uno Eins Unit Odd Un 2 Two Dos Zwei Prime Even Deux 3
Three Tres Drei Prime Odd Trois 4 Four Cuatro Vier Power2 Even
Quatre 5 Five Cinco Fuenf Prime Odd Cinq 6 Six Ses Sechs Composi
Even Six
[0140] Instead of creating separate columns in the displacement,
instance and occurrence tables for the FRENCH column, the FRENCH
column is "attached" to one of the other columns, whose
displacement, instance, and occurrence tables were shown
earlier.
[0141] First, a column is selected to which to "attach" the FRENCH
column; any column in the database may be selected for this
purpose. In this example, the PARITY column has been selected. When
reconstructing the records in the database, the appropriate value
for the "FRENCH" attribute is retrieved while determining the
"PARITY" value for that record.
[0142] In order to attach the FRENCH column to the PARITY column,
prior to "value-table condensation", the FRENCH cells in the value
table are sorted in the same order as the PARITY cells. As this
operation is performed during the construction of the data
structures in accordance with the present invention, a negligible
amount of additional effort is required. The sorted FRENCH column
is then appended to the condensed value table, as shown below:
[0143] Value Table:
TABLE-US-00016 Row ENG- # LISH SPANISH GERMAN TYPE PARITY FRENCH 1
Five Cinco Drei Composi Even Deux 2 Four Cuatro Eins Power2 Odd
Quatre 3 One Dos Fuenf Prime Six 4 Six Ses Sechs Unit Un 5 Three
Tres Vier Trois 6 Two Uno Zwei Cinq
[0144] The displacement, instance, and occurrence tables are, in
one embodiment, as follows:
[0145] Displacement Table:
TABLE-US-00017 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 1 1 2 2 4
3 3 4 6 5 6
[0146] Instance Table:
TABLE-US-00018 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 1 3 3 1 6
2 2 5 4 1 2 3 6 6 3 2 4 4 4 4 1 2 3 5 5 1 2 1 5 6 3 2 3 2 1
[0147] Occurrence Table:
TABLE-US-00019 Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 1 3 2 1 2
3 2 2 4 1 3 5 1 1 6 3 1
[0148] Now, for example, the record corresponding to the query
ENGLISH="Three" is reconstructed. This record, in the prior art
database, is given by:
TABLE-US-00020 Record ENG- # LISH SPANISH GERMAN TYPE PARITY FRENCH
3 Three Tres Drei Prime Odd Trois
[0149] To reconstruct this record from the data structures above,
first the value "Three" in the ENGLISH column of the value table is
found, and then the remaining attributes in the record are
reconstructed by tracing through the instance table. At the
instance cell for the Parity column, the "FRENCH" value
corresponding to the record is the value in the corresponding cell
of the FRENCH column in the value table. In the example, the entry
in row 5 of the Parity column of the instance table is associated
with the record being reconstructed. Thus, the "French" value is
found in row 5 of the "French" column of the value table, whose
value is "Trois".
[0150] Alternatively, an unsorted column may be included in the
data structures of the present invention by using the identity
permutation as the permutation for that column (i.e., the value
table for that column will not be reordered in any way).
Column Merge Compression
[0151] In accordance with a further embodiment of the invention,
separate value table columns can be merged into a single column,
referred to herein as a "union column," with separate displacement
list columns for each of the original columns. This has the
potential advantages of having a smaller value table, pre-joined
data expediting join operations and improved update speed. A value
not present in a particular original column is indicated in the
displacement table column by a null range for that value. For
example (assuming a "first row number" format displacement table),
if the original column did not have the value at row `r` of the
merged column, the displacement table for that column would have
the same value at row `r` and row `r+1` (that is
Displacement_Table(r+1,c)-Displacement_Table(r,c)=0). If `r` is the
last row in the column, its value is set to a number greater than
the number of rows in the instance table for that column.
[0152] Alternatively, if the displacement table is in "last row
number" format, the null range indicating no instances of value
number r is given by Displacement_Table(r,c)=Displacement_Table(r
1,c) (if r 1 is a valid row number), or, for r equals the lowest
valid row number, Displacement_Table(r,c)=0 (for 1-based row
numbering) or -1 (for zero-based row numbering).
[0153] For example, the following prior art database is
considered:
[0154] Prior Art Database:
TABLE-US-00021 Record # FIRST MIDDLE LAST 1 John Frederick Jones 2
Steven Allen Smith 3 Frederick Henry Blubwat 4 Albert Allen Brown 5
Alexander Graham Bell 6 Alexander The Great 7 Harvey Nelson Tiffany
8 Nelson Harvey Tiffany 9 Jackson Albert Poole 10 Henry Edward
Billings 11 Joseph Blubwat
[0155] The corresponding value and displacement tables for the
FIRST and MIDDLE columns are, in one embodiment:
Value Table:
TABLE-US-00022 [0156] Row # FIRST MIDDLE 1 Albert 2 Alexander
Albert 3 Frederick Allen 4 Harvey Edward 5 Henry Frederick 6
Jackson Graham 7 John Harvey 8 Joseph Henry 9 Nelson Nelson 10
Steven The
Displacement Table:
TABLE-US-00023 [0157] FIRST MIDDLE 1 1 2 2 4 3 5 5 6 6 7 7 8 8 9 9
10 10 11 11
[0158] Applying the column-merge space-saving technique results in
a single value table column for FIRST and MIDDLE, with the
displacement table columns for FIRST and MIDDLE adjusted to point
into that column, as shown below:
Value Table with Union Column:
TABLE-US-00024 FIRST union MIDDLE Albert Alexander Allen Edward
Frederic Graham Harvey Henry Jackson John Joseph Nelson Steven
The
Displacement Table
TABLE-US-00025 [0159] FIRST MIDDLE 1 1 1 2 2 3 4 3 4 5 4 6 5 7 5 8
6 9 7 10 8 10 9 10 10 10 11 11 12 11
[0160] In this embodiment, the absence of a blank FIRST name is
indicated by the first two rows of the displacement table having
the same value (i.e., the difference is zero). The absence of FIRST
name values "Allen" and "Edward" and MIDDLE name values
"Alexander", "Jackson, "John", "Joseph", and "Steven" are similarly
indicated. In addition, a FIRST name spelled "The" has no
occurrences, as is indicated by a displacement table value of 12,
which is greater than the number of records. Conversely, a
displacement table value in the last row that is less than or equal
to the total number of records indicates that value has an
occurrence (such as "The" in the last row of MIDDLE name in this
example).
[0161] In this example, if 20 bytes of storage is required for each
FIRST and MIDDLE field entry, uncondensed columns would use 440
bytes for 11 records. After column merge compression, the union
column of the value table uses a total of 20*15 bytes and, with
2-byte values in the displacement table, the displacement table
columns use 2*2*15 bytes, for a total of 360 bytes, a space savings
of 80 bytes. The space savings would be correspondingly greater
where the value table values for the separate columns have more
overlap. Union columns can also be advantageously used in
implementing joins, as described below.
[0162] Another space saving technique used in alternate embodiments
of the present invention is to combine fields of low cardinality
into a single field having values representing the various
combinations of the original fields. For example, in the example
above, the TYPE and PARITY fields can be merged into a single
field, TYPAR, having values representing combinations of TYPE and
PARITY values.
[0163] Modified Input Table:
TABLE-US-00026 Record # ENGLISH SPANISH GERMAN TYPAR 1 One Uno Eins
Odd_Unit 2 Two Dos Zwei EvenPrime 3 Three Tres Drei Odd_Prime 4
Four Cuatro Vier EvenPower2 5 Five Cinco Fuenf Odd_Prime 6 Six Ses
Sechs EvenComposite
Value Table:
TABLE-US-00027 [0164] Row # ENGLISH SPANISH GERMAN TYPAR 1 Five
Cinco Drei EvenComposite 2 Four Cuatro Eins EvenPower2 3 One Dos
Fuenf EvenPrime 4 Six Ses Sechs Odd_Prime 5 Three Tres Vier
Odd_Unit 6 Two Uno Zwei
Displacement Table:
TABLE-US-00028 [0165] TYPAR 1 2 3 4 6
[0166] Instance Table:
TABLE-US-00029 Row # ENGLISH SPANISH GERMAN TYPAR 1 1 3 4 4 2 2 5 6
2 3 6 6 5 6 4 4 4 1 5 5 5 1 2 1 6 3 2 3 3
[0167] The process of setting up these data structures is exactly
as before, except that the TYPE and PARITY data is taken as a unit,
rather than being two separate columns. While the compression of
the TYPAR column is less than the compression achieved for the
original TYPE and PARITY columns (due to the greater number of
distinct values), an overall savings of space results due to the
reduced numbers of columns in the displacement and instance tables.
This space savings is realizable if the combined cardinality is
sufficiently low. Searching for values matching the first part of
the combined field (Even/Odd) is generally unchanged, but searching
for the second part (Composite/Power2/Prime/Unit) is more
complicated. To search for, for example, "Prime" it is necessary to
search for both "EvenPrime" and "OddPrime". In general, C such
searches will be necessary, where C is the cardinality of the first
column of the combination. Counts are also more complicated for
either column involved. More than two columns may be combined, with
similar costs.
Hashing
[0168] Hashing comprises a known high-speed data storage and
retrieval mechanism that can significantly outperform
logarithmic-time binary searching. Although capable of delivering
low-coefficient constant-time performance when implemented with an
efficient hash function on an appropriate size hash table, the
search for high-performance hash parameters can be complex,
difficult and data dependent (e.g., depending on both the number
and distribution of values). Still more importantly, hashing has
major drawbacks--especially as implemented by state of the art
DBMS's. Hash functions typically fail to return ordered results
rendering them unsuitable for range queries, user requests for
ordered output, such as SQL "sort-by" and "group-by" queries, and
other queries whose efficient implementation is dependent on
sortedness, such as joins.
[0169] By supporting an efficient, ordered, reduced-space
representation of multi-dimensional data, the present invention
obviates the deficiencies of hashing associated with the
unorderedness of prior art DBMS's. Moreover, any known hashing
technique can be used in conjunction with, and as part of, the
present invention.
[0170] One example of hashing applied to a sorted value table is a
64 KB hash table in which each entry in the hash table contains the
position of the first element in the value table whose first two
bytes match the entry's position. For example, using O-based
numbering, the first entry in the hash table contains a pointer to
the first entry in the value table whose first two bytes contain
all 0's. The second entry contains a pointer to the first entry in
the value table whose leading two bytes contains 00000000 00000001,
and so on. Every set of consecutive hash table entries thus
uniquely specifies the entire range of values containing the
associated leading two-byte bit-pattern for all 64 k possible
leading two-bytes. This narrowed range of values can then be
searched, via for example a binary search, to find any sought
value. Two consecutive hash table entries with the same value
indicates that no value elements contain the leading two bytes of
the first entry.
[0171] Additional modifications can be imposed on top of hash
tables implemented as described above. For example, space can be
saved by stripping off the specified two bytes of the values in the
value table, because those bytes can be obtained from the hash
table. However, additional time is then needed to reconstruct the
leading stripped off two bytes (if not known from the lookup),
before that value can be returned to the user. This may be done for
example by binary searching the hash table for the appropriate row
in the value table. This may take up to 16 additional steps for a
64 k hash table in the worst case, but average performance can be
significantly reduced by for example an interpolation search where
this is supported by the regular distribution of a particular data
set.
[0172] Hashing may also be performed on instance elements to
directly return or narrow the search for an associated value
element, serving as an alternative to the occurrence table. Any
hash function that returns the value element associated with a
given instance element or some near-by value element can be used
for this purpose. If a near-by value element is returned, the
specific associated value element is then found by searching a
limited portion of the displacement table. One such technique is a
64 KB hash table with pointers into the value table mapped onto
each possible leading two bytes of an instance table. The range of
displacement table entries to search are given by a hash table
entry and its adjacent entry.
[0173] In situations where significant searching is still required
but utilizable localized distribution patterns also exists this 64
KB entry hash table may be modified to accept two part entries. In
such an implementation the first hash table entry still points to
the first value associated with the first instance element that
contains the two leading bytes specified by that position in the
hash table. The second hash table entry then provides the address
of a function that utilizes this local distribution to further
narrow the search for the value element associated with that
specified instance element.
[0174] The choice of 64 KB hash tables corresponding to two byte
fields is not meant to be inclusive. Other byte size choices, other
radixes, and byte placements other than the leading bytes can also
be utilized. Moreover, any other known hashing method may also be
used.
A General Case Topology for the Instance Table
[0175] As described above, in a specific embodiment, individual
records are linked through the instance table in some topology, one
of the simplest of which is a circularly linked list, or "ring"
topology. So far the examples have used this simple ring
topology--the pointers (i.e., entries) in the instance table link
all the fields in a record in a single loop with each field having
a single "previous" and a single "next" field, as shown in FIG. 2.
Other topologies may be used in other embodiments of the
invention.
[0176] A topology, as the term is used in connection with the
present invention, is defined in terms of a graph in which
attributes (or other forms of associated data) are nodes in the
graph and links exist between nodes. Such is clearly the case for
the simple ring topology.
[0177] Another example of a topology is shown in FIG. 3. In this
topology, the fields are separated into two subsets having exactly
one field in common and each subset having a simple ring topology.
The field common to both rings acts as a "bridge" between them.
Complete record reconstruction then requires traversal around both
rings, with the bridge field joining the record's subrings into a
single entity. This topology is particularly useful if the majority
of queries only pertain to the fields in one of the subrings, since
that subring can then be traversed and retrieved without traversing
and retrieving the full record.
[0178] As shown in FIG. 4, still another topology is a star, or
spur, configuration, wherein each field represents a doubly-linked
spoke radiating from a central hub. Alternatively, the individual
spurs (branches) of the star may be either a linear or ring
topology. In general, any of the above topologies could be combined
(or other topologies used) to optimize record storage and retrieval
for specific databases.
[0179] Any defined topology may be either singly or doubly linked
and a topology need not be closed as in the examples above. Also, a
topology may be changed between singly and doubly linked at the
user's option or automatically by the database system based on
access patterns. A doubly-linked topology is useful when adjacency
of data is important; that is, when the order of the fields in the
record is arranged such that fields frequently accessed in
combination are located topologically close to each other.
Singly-linked topologies are more desirable when full records (or
substantial portions of them) are retrieved, or if a predominant
field-retrieval starting point and order are given, since the
instance list in a singly-linked topology occupies half the storage
of the doubly-linked case.
Bridge Field Example
[0180] FIG. 3 specifically illustrates a topology wherein each
record is comprised of two separate subrings
(ENGLISH>SPANISH->GERMAN and ENGLISH->TYPE->PARITY)
with ENGLISH as the bridge field. An instance table that implements
such a topology is shown below:
TABLE-US-00030 Row # ENGLISH SPANISH GERMA TYPE PARITY 1 1/5 3 5 3
6 2 2/2 5 3 2 2 3 6/6 6 1 1 4 4 4/1 4 4 5 3 5 5/4 1 2 6 5 6 3/3 2 6
4 1
[0181] The ENGLISH column has two outgoing pointers, one for each
of the subrings. To traverse, for example, the record starting in
row 1 of the ENGLISH column, one of the outgoing pointers is first
followed, for example, the one pointing to row 1 of the SPANISH
column. Row 1 of the SPANISH column points to row 3 of the GERMAN
column, which in turn points back to row 1 of the ENGLISH column.
The other outgoing pointer is then followed, leading to row 5 of
the TYPE column. Row 5 of the TYPE column in turn points to row 6
of the PARITY column, which again points back to row 1 of the
ENGLISH column.
Database Implementation
[0182] Described below are implementations of routines for
inputting data to, maintaining, and extracting data from the data
structures described above. A person skilled in the art will
recognize that there are many different algorithms for performing
these operations, and the present invention is not limited to the
algorithms shown herein.
[0183] Primitive functions (i.e., functions that are called by
other functions) are provided, in one embodiment, to extract the
data associated with a given record and buffer it in linear form,
and to write such a buffered linear form of the data back into the
data structures of the invention.
[0184] Data structures in accordance with the present invention are
referred to below as follows:
[0185] 1) VALS2: a value table with the columns in sort order and
possibly condensed;
[0186] 2) DISP: displacement table (column I of which has same
number of rows as the corresponding column I of VALS2);
[0187] 3) DELS: deletes table, described below, (column I of which
has same number of rows as the corresponding column I of
VALS2);
[0188] 4) INST: instance table;
[0189] 6) OCCUR: occurrence table.
[0190] In the discussion below, an embodiment having a ring
topology is used, unless otherwise noted. In the ring topology in
this embodiment, the functions prev(C) and next(C), which return
the previous and next column, respectively, are as follows:
prev(C)=(C+fcount-1) mod fcount, and next(C)=(C+1) mod fcount,
where fcount is the number of columns and C is a column number
ranging from 0 to fcount-1. An alternate embodiment has column
numbers ranging from 1 to fcount, with prev(C)=(C-1)?(C-1):fcount
(using C language notation), and next(C)=C mod fcount+1. More
general topologies may be implemented by defining more complicated
prev( ) and next( ) functions, and/or by analysis of the topology
into simple rings and repeated application of the functions below
on those simple rings.
[0191] The number of rows in the uncondensed value table, and the
instance table, is represented as reccount. Condensed VALS2 columns
will have fewer rows, as will the corresponding DISP and DELS
structures. Rows are numbered from 0 to reccount-1 (zero-based);
alternate embodiments may have rows numbered from 1 to reccount
(one-based).
[0192] "V/O splitting" refers to the alternative instance table
with condensed value table discussed above--the Ith column is
called "V/O split" if the pointers in column I of the instance
table have both a value and an occurrence component. Parallel
treatments for non-V/O and V/O split columns are presented where
appropriate. The descriptors for each column in the instance table
indicate whether the column has V/O splitting. The descriptors also
contain other column/attribute specific information, such as the
path of node traversal (i.e., "record topology"), whether the
column has O-based or 1-based numbering, etc.
[0193] Column descriptors for each column of the value table
contain configuration information, such as its data type, size of
field, type of permutation/change (e.g. grouped by value, sorted),
type of compression (if any), locking information, type of hashing
(if any), and etc.
[0194] Other tables also have column descriptors containing
relevant configuration information.
[0195] To facilitate the notation of function variables and return
values, the following will be used (written in a pseudo-C/C++
notation):
[0196] typedef long Row;
[0197] typedef int Column;
[0198] class ChainVO {Row chainv[fcount]; Row chainO[fcount]; bool
valid;}
[0199] If a ChainVO object has been filled in with data for a valid
record, chainV[C] contains the row number of the record's VALS2
entry in column next(C).
[0200] If column C of the instance table is V/O split, chainO[C]
contains the occurrence number of the value VALS2[chainV[C],
next(C)].
[0201] If column C of the instance table is not V/O split,
chainO[C] contains the row number of the record's cell in column
next(C) of the instance table(s).
Record Reconstruction
[0202] Given a row number R in column C of the instance table,
there exists a unique row number V in VALS2, containing the actual
value associated with the [R,C] cell of the instance table. The
routine shown in FIG. 5, Row get_valrec(Row R, Column C),
determines V from R and C. Step GV1 determines whether column C has
a DISP table column by checking the column descriptors for column
C, and if not, step GV2 sets V to R. Otherwise, if a DISP table
column is present, step GV3 determines its format (again by
checking the column descriptor). If the DISP table column is in
first row number format, then V is set, in step GV4, to the value
for which DISP[V,C]<=R<DISP[V+1,C] is true, where the
upper-bound test is not performed if V+1 does not exist (i.e., if V
is the last DISP table row for column c). Otherwise, V is set, in
step GV5, to the value for which DISP[V-1]<R<=DISP[V,C],
where the lower-bound test is not performed if V-1 does not exist
(i.e., if V is the first DISP table row for column c).
[0203] If column C of the instance table is V/O split, row number
Next_R in column next(C) of the instance table is determined from
the V/O entries in a manner dependent on the DISP and OCCUR
implementation as shown in the flowchart of the R_from_VO(C, I, O)
routine in FIG. 6. R_from_VO( ) is passed the current column, C,
the row number, I, of the associated value in the next column,
next(C), of VALS2 (and DISP) and the occurrence number, O, of that
value. Step 242 sets variables I' to I and X to zero. Step 243
tests (e.g., via column descriptors) whether column next(C) of the
DISP table is in "first row" format or "last row" format. If it is
"last row" format, step 244 is performed, which sets I' to I-1 and
X to 1. In either case, step 245 is then performed, which sets
variable O' to O. Step 246 is then performed, which tests whether
column C of the OCCUR table is 1-based. If it is, step 247 is
performed, which sets O' to O-1. In either case, step 248 is then
performed, which sets Next_R, the row in the next column, to
DISP[I',next(C)]+O'+X].
[0204] FIG. 7 illustrates a function for linearizing a record's
topology data, referred to herein as get_chain(Row R0, Column C0).
Starting at row R0, column C0 in the instance table, this routine
walks through the pointer cycle, storing the pointers in a ChainVO
object. If the pointer cycle closes, ChainVO.valid is set to
"true"; otherwise it is set to "false".
[0205] In step G1, instance table cell [R0, C0] is set as the
starting point for record reconstruction. In step G2, the "current
cell" [R, C] is initialized to the starting cell [R0, C0]. In step
G3, the column descriptors for the current column in the instance
table are checked to see if it has V/O splitting.
[0206] If the column does not have V/O splitting, step G4 fetches
the row number in the next column directly by setting R to INST[R,
C]. Step G5 sets the variable O for loading into the chainO[ ]
array. Step G6 uses get_valrec(R, next(C)) to find the
corresponding next-column row number, V, in VALS2, DISP, and DELS
(if they exist).
[0207] If column C has V/O splitting, V (the row number in the next
column, next(C), of VALS2, DISP, DELS) and O (the occurrence number
for that value) are set, at step G7, to INST[R, C] and OCCUR[R, C],
respectively. Step G8 then uses R_from_VO(C, V, O) as described
above to find the row number, R, in column next(C) of the instance
table.
[0208] Processing then reconverges at step G9, where chainV[C] and
chainO[C] are set to V and O, respectively. Step G10 then replaces
C with next(C), and step G11 checks to see if processing has
returned to the column at which it started (i.e., C0). If not,
processing loops back to step G3, and repeats as above. If
processing has reached the original starting column, step G12
compares the current value of R to the starting value R0. If equal,
the pointer chain forms a closed loop, indicating that a valid
record has been reconstructed and stored in the ChainVO object, and
step G14 sets a flag to indicate this. If R is not equal to R0,
step G13 sets a flag to indicate the attempt to reconstruct a
record did not result in a closed loop, which in this embodiment of
the invention (which uses a ring topology) indicates that a valid
record does not pass through cell [R0, C0]. In other embodiments of
the invention, using different topologies, the pointer chain
between associated instance elements need not form a closed
loop.
[0209] The final step of record reconstruction is the conversion of
the value table row numbers stored in the chainV array to values.
The column C value of the record is given by VALS2[chainV[prev(C)],
C] (possibly with a hash value prefixed, as described above).
Generalized Record Reconstruction
[0210] The description above for using get_chain( ) to reconstruct
a record is based on a simple loop topology in which the next
column in the topology depends only on the current column. The
situation may be generalized. The next column may depend on
meta-data, other than or in addition to the current column. For
example, the next column might be a function of both the current
column and the previous column, i.e., C=next(C, prev(C)). In
addition, the next column in the topology may depend on data
itself, such as the value, V, of the current cell in the value
table, or depend on all of the above, i.e., C=next(C, prev(C),
V).
Primitives for Record Modification
[0211] Primitive functions are now described for one implementation
of record deletion, record insertion, and record modification. The
implementation is referred to herein as the "swap" method. In this
method a value in the value table may have deleted as well as
nondeleted ("live") instances. A data structure, referred to herein
as DELS, stores a count for each value of the number of deleted
instances it has. Thus, DELS has the same number of columns as
VALS2 and DISP, and, for any given column, the same number of rows
in that column as VALS2 and DISP. The deleted instances are
regarded as free space in the instance table, and the instance
table is maintained such that for any given value in any given
column, all live instances are grouped contiguously together and
all deleted instances are grouped contiguously, such that the live
instances precede the deleted instances or vice versa. This permits
free space to be easily located for assignment to new records or
new field values for existing records, as shown in the functions
below. Free spaces can also be placed at desired locations in the
instance table at setup time by including appropriate deleted
records in an input data table; thus providing one implementation
for performing insertions prior to deletions.
[0212] The put_chain(Column C0, ChainVO rec, int count) function,
shown in FIG. 8, performs the inverse of get_chain( ). Put_chain(
), starting in column C0, writes part or all of the contents of a
ChainVO object "rec" into the instance and occurrence tables, for
"count" number of columns. The row number written to in column C is
obtained from the prev(C) entries in rec. Put_chain( ) does not
modify the value or displacement tables.
[0213] Step P1 sets the current column number C to the starting
column C0. Step P2 checks the column descriptors for the instance
table at column prev(C) to determine whether the previous column is
V/O split. If prev(C) is V/O split, step P3 sets V (the row number
in the value and displacement tables) to chainV[prev(C)] and O (the
row number in the occurrence table) to chainO[prev(C)]. Step P4
sets R (the row number in the instance table) to
R_from_VO(prev(C),V,O).
[0214] If the prev(C) column of the instance table is not V/0
split, step P5 sets R to chainO[prev(C)]. Having now obtained the
row number in column C of the instance table at which to write,
step P6 determines if column C is V/0 split. If it is not, step P7
sets INST[R,C] to chainO[C]. If column C is V/0 split, step P8 sets
INST[R,C] to chainV[C] and OCCUR[R,C] to chainO[C]. Processing then
moves on to the next column in step P9 and the count of columns to
process is decremented in step P10. If step P11 determines that no
additional columns are to be written, processing is done, otherwise
processing loops back to step P2 and repeats.
[0215] FIG. 9 is a flowchart of the function int swap(Column C, Row
R1, Row R2), which modifies the instance table, and other tables,
such that the record passing through [R1,C] is made to pass through
[R,C], and the record passing through [R2,C] is made to pass
through [R1,C].
[0216] Step S1 fetches the record data for the record passing
through INST[R1,C] into ChainVO object ChainVO_1 and fetches the
record data for the record passing though INST[R2,C] into
ChainVO_2. Both records must be closed loops, otherwise, an
exception is raised by get_chain( ). If both loops are valid, in
step S2, the values in ChainVO_1.chainV[prev(C)] and
ChainVO_2.chainV[prev(C)] are interchanged and the values in
ChainVO_1.chainO[prev(C)] and ChainVO_2.chainO[prev(C)]
interchanged. The exchanged values are in the prev(C) column,
because that column determines the row number of column C in the
instance table. The modifications are then written back into the
instance table in step S3 via the calls to put_chain(prev(C),
ChainVO_1, 2) and put_chain(rev(C), ChainVO_2, 2). Put_chain) is
called with count 2, since one pass through the put_chain( ) loop
updates the pointers to the swapped cells, and the second pass
updates the contents of the swapped cells. A success code is
returned in step S4, and processing is complete.
[0217] FIG. 10 is a flowchart of the function del_swap(Column C,
Row R, Row Rd), which modifies the instance and other tables such
that the record through [R, C] is rerouted to pass through free
cell [Rd, C]. This routine is used, for example, in maintaining
segregation of deleted from live instances of a given value.
[0218] In step D1, data for the record to be rerouted (at row R,
column C) is placed in the ChainVO object ChainVO_r via a call to
get_chain( ). If get_chain( ) determines that the record is not a
closed loop (i.e. it is an invalid record), an exception is raised.
Step D2 finds the row, Vd, of the value table associated with the
free cell Rd, using Vd=get_valrec(Rd, C).
[0219] Step D3 checks the column descriptors for column prev(C) of
the instance table to determine if it is V/O split. If it is not
V/O split, step D4 is performed, which sets
ChainVO_r.chainV[prev(C)] to Vd and ChainVO_r.chainO[prev(C)] to
Rd. If column prev(C) is V/O split, steps D5 and D6 are performed.
Step D5 sets the occurrence number, Od, in a manner closely related
to R_from_VO( ) described above; specifically, Od=Rd DISP[Vd', C] X
(where Vd'=Vd and X=0 if DISP is "first row number" format, or
Vd'=Vd 1 and X=1 if DISP is "last row number" format; if OCCUR is
1-based rather than zero-based, decrement X by 1 in the preceding).
Step D6 puts values into the ChainVO object, setting
ChainVO_r.chainV[prev(C)] to Vd and ChainVO_r.chainO[prev(C)] to
Od. In either case, step D7 is then performed, which writes the
modified record topology back into the instance table, via a call
to put_chain(prev(C),ChainVO_r,2), and processing is complete.
[0220] FIG. 11 is a flowchart of the function top_undel(Column C,
Row R). Cell [R,C] of the instance table has associated value
VALS2[V, C], where V=get_valrec(R,C). If this value has live
instances, top_undel( ) returns the highest row number (in the
instance table column C) for such live instances; otherwise the
routine returns a flag indicating there are no live instances and a
number that is one less than the row number of the first instance
of V.
[0221] In step T1, the value table row V associated with instance
table row R of column C is found; i.e., V=get_valrec(R, C). Step T2
sets UP to the highest row number in the instance table of all
instances of value V. If DISP is in "last row number" format,
UP=DISP[V,C]; if DISP is "first row number" format, UP=DISP[V+1,C]
1, if DISP[V+1,C] exists, or, if DISP[V+1,C] does not exist,
UP=reccount+X 1 (where X=0 for 0 based row numbering, and X=1 for 1
based row numbering). If there is no DISP at all for column C, a
search through the uncondensed value table column will provide the
row numbers of the first and last instances of value number V. Step
T3 sets DLS to the count of deleted instances for value number V.
If there is a DELS structure, DLS=DELS[V,C]; otherwise, DLS is
obtained by counting the instances flagged as deleted. Step T4 sets
TU to the row number immediately previous to the first deleted
instance of value number V (again, in the "swap method" embodiment
all live instances of value number V precede, or in an alternate
embodiment follow, all deleted instances of that same value). Step
T5 sets BOT, the row number of value number V's first instance. For
"first row number" format DISP, BOT=DISP[V,C]; for "last row
number" format DISP, BOT=1+DISP[V 1,C] (if DISP[V 1,C] exists), or
BOT=X (for X based row numbering, X=0 or X=1). If there is no DISP
for column C, then BOT is obtained by a search in the uncondensed
value table. Step T6 tests to see if TU>=BOT. If not, then row
number TU does not belong to value number V, but instead is one
less than the row number of the first instance of V. Step T7
follows, returning TU and a flag indicating that all instances are
deleted. If TU>=BOT, step T6 is followed by step T8, which
returns the desired row number.
[0222] FIG. 12 is a flowchart of the function
I_move_space_uplist(Column C, Row V), which swaps pointers in the
instance table, so as to move a free cell from DELS[V+1, C] to
DELS[V, C] while maintaining the segregation of live from deleted
instances.
[0223] Step U1 checks whether there exists a value in row number
V+1 in column C of VALS2. If there is no such value in row number
V+1 (i.e., index V+1 is out of bounds), an error is reported at
step U2 and function is done. Otherwise, step U3 tests whether
value row V+1 of column C of VALS2 has any deleted instances (one
of which will be moved by this routine). If it has none, step U4
reports an error (no spaces to move), and processing terminates. If
deleted instances are found, step U5 tests whether value row V+1
has any live instances by calculating J=top_undel(C, K) (where K,
the row number of the first instance of value number V+1, is given
by K=DISP[V+1,C] if column C of DISP is "first row number" format,
or K=DISP[V,C]+1 if column C of DISP is "last row number" format,
or is found e.g. by linear search in the values table if there is
no column C of DISP). If so, step U6 calls del_swap(C, K, J+1) to
swap the first live instance (at row K) with the first deleted
instance (at row J+1), thereby putting the free cell next to the
instance table rows associated with the value V. Step U7 then
deducts this free cell from the count of deleted cells for value
number V+1 (by decrementing DELS[V+1,C] if DELS has a column C),
step U8 adds the cell to the count of deleted cells for value
number V (by incrementing DELS[V,C], if DELS has a column C), and
step U9 adjusts the Displacement table (if it has a column C), to
reflect the transfer of the free cell into value number V's set of
deleted instances. If column C of DISP is in "first row number"
format, DISP[V+1,C] is incremented to move the "floor" of the
instance block for value number V+1 up one cell; if column C of
DISP is "last row number" format, DISP[V,C] is incremented to move
the "ceiling" of the instance block for value number V up one
cell.
[0224] FIG. 13 is a flowchart of I_move_space_downlist(Column C,
Row V), which swaps pointers in the instance table, so as to move a
free cell from DELS[V, C] to DELS[V+1, C]. Segregation of live from
deleted instances is maintained. An error is indicated by the
return value.
[0225] Step W1 determines whether row V+1 of column C of VALS2 is
out of bounds. If it is, step W2 reports an error (i.e., that there
is no V+1 value to move a free cell to) and returns. Otherwise,
step W3 tests whether value V has any deleted instances (one of
which will be moved by this routine). If not, step W4 reports an
error (no spaces to move), and processing terminates. If deleted
instances are found, step W5 calculates J=top_undel(C, K) (where K,
the row number of the first instance of value number V+1, is given
by K=DISP[V+1,C] if column C of DISP is in "first row number"
format, or K=DISP[V,C]+1 if column C of DISP is in "last row
number" format, or is found e.g. by a linear search in the values
table if there is no column C of DISP) to determine whether value
number V+1 has any live instances. If it does, step W6 calls
del_swap(C, J, K-1) to swap the top live instance (at J) of value
V+1 with the last deleted instance of value V (at K-1), thereby
moving the free cell to the instance table rows associated with
value table row number V+1. Step W7 then adds this free cell to the
count for value number V+1. Step W8 deducts the cell from the count
for value number V. Step W9 shifts the boundary between V and V+1
to incorporate the transferred free cell into value number V+1's
set of deleted instances. If column C of DISP is in "first row
number" format, DISP[V+1,C] is decremented to move the "floor" of
the instance block for value number V+1 down one cell; if column C
of DISP is "last row number" format, DISP[V,C] is decremented to
move the "ceiling" of the instance block for value number V down
one cell.
[0226] FIG. 14 is a flowchart of Row inst_count(Column C, Row V),
which gets the total instance count (live+deleted) for the value at
VALS2[V, C], where V is a row number in the VALS2 array and C is
the column number.
[0227] Step C1 determines if column C of DISP exists. If it does
not, entries of the required value in the uncondensed values column
are counted directly in step C2, and processing is complete. If
column C of DISP does exist, step C3 determines if the DISP column
is in "first row number" format. If it is not, processing continues
with step C4. If the DISP column is in "first row number" format,
processing continues with step C8. Step C4 determines how to set
the variable BOT: if V is the lowest allowed index for DISP, then
step C5 sets BOT=-1 for 0 based row numbering, or sets BOT=0 for 1
based row numbering. If on the other hand V1 is a valid index for
DISP, step C6 sets BOT=DISP[V 1,C]. Step C7 then finds the total
instance count as DISP[V,C] BOT, and processing is complete. If
step C3 determines that DISP[c] is in "first row number" format,
processing goes to step C8, which determines how to set the
variable TOP: if V is the highest allowed index for DISP, then step
C9 sets TOP=reccount+X for X based row numbering (X=0 or X=1). If
on the other hand V+1 is a valid index for DISP, step C10 sets
TOP=DISP[V+1,C]. Step C11 then finds the total instance count as
TOP DISP[V,C], and processing is complete.
[0228] FIG. 15 is a flowchart of a function that deletes the
instance table cell [R,C]; that is, cell [R,C] in the instance
table is placed in the free pool, and the appropriate DELS count is
incremented. If the newly deleted cell is surrounded by live cells
for the same value, it is moved to the live/deleted boundary via
del_swap( ). The record's topology data is in a ChainVO object
called VO. This routine is used in record deletion and in updating
a field in an existing record; see "Update existing record" step E6
and "Delete record through cell" step DR7, below.
[0229] In step DC1, the VALS2/DELS/DISP row number in column C is
obtained from the ChainVO structure representing the record being
processed, and the corresponding DELS count is incremented. Step
DC2 determines whether the pointers to the cell in question are V/O
split. If prev(C) is not V/O split, step DC3 gets the row number R
directly from VO.chainO. If prev(C) is V/O split, step DC4
reconstructs R from VO.chainO via
R=R_from_VO(prev(C),V,VO.chainO[prev(C)]). In either case, the top
undeleted cell for the same value is located, via a call to
top_undel(C,R), and set to T in step DC5 (which is guaranteed to
exist, since the cell to be deleted is such an undeleted cell).
Step DC6 then tests whether the cell being deleted is the topmost
undeleted cell for the value in question. If not, a swap is
performed in step DC7 via a call to del_swap(C,T,R) in order to
maintain segregation of live from deleted instances. Processing is
then complete.
[0230] FIG. 16 is a flowchart of insert_v(Row V, Column C, void
*newvalptr), which inserts into column C of VALS2, at row V, a new
value not previously present (pointed to by newvalptr), and
modifies the associated DELS and DISP tables (if they exist) to
accommodate the new value. This function is used only when column
prev(C) of the instance table is not V/O split.
[0231] Step IV1 tests whether the value at the insertion point (row
V) has any live instances; i.e., whether top_undel(R,C) returns a
flag indicating that there are no live instances (R here is the
INST row number of any instance of value number V; if column C of
DISP exists, R=DISP[V,C] is such an instance; if DISP has no column
C, R=V is such an instance. If there are no live instances of the
value at row V, step IV2 is performed, which overwrites the old
value with the new value, and processing is complete. If there is a
live instance, a search is performed for the closest value having
no live instances. Step IV3 initializes an index J to 1. Step IV4
determines whether both V+J and V-J are out of bounds. If they are,
meaning that no further searching is possible and no free value
slots have been found, step IV5 is performed which allocates
additional space, for one or more additional slots, in column C of
VALS2, DISP and DELS. Step IV6 tests whether V+J is in bounds, and
whether the value at row V+J has any live instances (via
top_undel(R',C), where R' is the INST row number of any instance of
value number V+J; if column C of DISP exists, R'=DISP[V+J,C] is
such an instance; if DISP has no column C, R'=V+J is such an
instance. If V+J is in bounds and value V+J has no live instances,
then the branch starting with step IV7 is executed; otherwise, step
IV10 is executed.
[0232] The branch starting with step IV7 is a loop which shifts the
values in rows V to V+J-1 in VALS2 to the next higher row, thus
opening an unused row at row V of VALS2. Step IV7 adds the deleted
instances of value number V+J to value number V+J-1, e.g., if DELS
has a column C, then DELS[V+J-1,C] is set to
DELS[V+J-1,C]+DELS[V+J,C]. Step IV8 shifts the values at row V+J-1
of VALS2, (and DELS and DISP, if they exist) to row V+J of VALS2,
DELS and DISP, respectively (i.e., VALS2 [V+J,C]=VALS2 [V+J-1,C];
DELS [V+J,C]=DELS [V+J-1,C]; DISP[V+J,C]=DISP[V+J-1,C]), and then
decrements J. Step IV9 iterates step IV8 until J=0. Then, step IV15
inserts the new value at row V of VALS2 and updates DELS and DISP
to indicate that the new value has no instances; i.e.,
VALS2[V,C]=new value, DELS[V,C]=0, and DISP[V,C]=DISP[V+1,C].
Processing is then complete.
[0233] Step IV10 tests whether V-J is in bounds, and whether the
value at row V-J has live instances. If there are live instances,
step IV11 is executed, which increments J and loops back to step
IV4. If V-J is in bounds and value number V-J has no live
instances, step IV12 is executed, which begins a loop which shifts
the values in rows V-J+1 to V in VALS2 to the next lower row, thus
opening an unused row at row V of VALS2. Step IV12 adds the deleted
instances of value number V-J to value number V-J-1 (e.g. if DELS
has a column C, then DELS[V-J-1,C] is set to
DELS[V-J-1,C]+DELS[V-J,C]). Step IV13 then shifts values for rows
V-J+1 of VALS2, (and DELS and DISP, if they exist) to rows V-J of
VALS2, DELS and DISP, respectively (i.e. VALS2 [V-J,C]=VALS2
[V-J+1,C]; DELS [V-J,C]=DELS [V-J+1,C]; DISP[V-J,C]-DISP[V-J+1,C]),
and decrements J. Step IV14 iterates step IV13 until J=0, at which
point step IV15 inserts the new value, with no instances, as
described above, and processing is complete.
[0234] FIG. 17 is a flowchart of insert_vov(Row V, Column C, void
*newvalptr), which inserts a new value (pointed to by newvalptr)
into column C of VALS2, when column prev(C) of the instance table
is V/O split. The set of column descriptors for such a column
includes a value h_val, the highest currently used row number in
VALS2 column C, and h_ptr, the highest currently used row number in
the instance table. Both VALS2 and the instance table are
preferably allocated with extra blank space at their ends to
accommodate new entries. In one embodiment of the present
invention, inserted new values are written at the end of the VALS2
table (rather than at their sort-order position, as in insert_v( ),
above). A permutation list giving the added VALS2 row numbers in
sort order is updated by insertion of the new indexes at their
proper sort positions. The permutation list is used to access the
new part of the VALS2 column in sort order (e.g., by a binary
search algorithm). A search for a value in the VALS2 column would
first search the original, sorted part of the value list and, if no
match was found, a second binary search would use the permutation
list to search among the new values.
[0235] Other means can be utilized to avoid otherwise unnecessary
searching of the appended new value list. These include, but are
not limited to, the following: (1) The original sorted value list
together with any instance table values for V/O splitting may be
re-organized in the background or overnight to keep the appended
new value list as short as possible; (2) A bit flag embedded in the
value list or associated displacement list or standing alone
identifies when new values have or have not been appended between a
given old value and a contiguous old value to avoid unnecessary
searching of the appended new value list when no new values fall
within that range; (3) A pointer mechanism, possibly associated
with an existing hash function or with a hash function used
expressly for this purpose narrows the range of the appended new
value list that needs to be searched.
[0236] The insert_vov routine is used by the "Insert new record"
and "Update existing record" routines.
[0237] Step VOV1 gets, from the column descriptors for column C,
h_val, the highest VALS2 slot number already used in column C, and
h_ptr, the highest instance table row number already used. In step
VOV2, h_val and h_ptr are incremented to point to the first
available empty slots in column C of VALS2 and the instance table,
respectively, if such empty slots exist. Step VOV25 determines if
h_val is in range and, if it is not in range, step VOV26 allocates
additional space, for one or more additional slots, in column C of
VALS2, DISP and DELS. Step VOV27 then determines if h_ptr is in
range and, if it is not, step VOV28 allocates additional space, for
one or more additional slots, in column C of INST.
[0238] In step VOV3, the VALS2 slot is filled in with the new value
(so that h_val once again indicates the highest used slot number);
i.e., VALS2[h_val,C] is set to new value. In step VOV4, the new
value's proper sort order position is found within the set of new
appended values, and the value h_val is inserted at that position
in the permutation list. In step VOV5, the DISP and DELS structures
are updated; DISP[h_val,C] is set to h_ptr, and DELS[h_val,C] is
set to 1, since incrementing h_ptr by one has in effect allocated
space for one record, which is not yet a "live" record, and is thus
part of the DELS pool. Finally, in step VOV6, row V, which is equal
to the sort position of the new value) is changed to h_val for
proper inclusion into the ChainVO object used in the routine
calling insert_vov( ) (specifically, chainV[prev(C)] must point to
the actual location of the new value, i.e. h_val).
[0239] FIG. 18 is a flowchart of insert_c(ChainVO VO, Column C).
This routine checks if there is a deleted instance of the column C
value specified by VO and, if not, migrates a deleted instance from
the nearest value having one. The row number of the first deleted
instance of the value is then stored in VO.chainO (either as offset
or row number, depending on V/O splitting).
[0240] Step IC1 sets V to the VALS2 row number in column C for the
value whose first deleted instance is to be written into
VO.chainO[prev(C)] (i.e., V=VO.chainV(prev(C)). Step IC2 determines
whether this value has a deleted instance (i.e., whether
DELS[V,C]>1, or by direct count of tombstoned, flagged, cells in
those embodiments in which deleted cells are marked by a flag). If
this value has no deleted instances, step 1C3 is performed, which
does an iterative search for the closest value with a deleted
instance (similar to the search done in "insert_v( )" above) to
determine whether there is a deleted instance for any value. If no
deleted instance is found, step 1C4 allocates additional space, for
one or more additional slots, in column C of INST, and adjusts the
data structures as needed to indicate that the additional slots are
free (i.e., deleted instances). Step 1C5 then does an iterative
application of I_move_space_uplist( ) or I_move_space_downlist( )
until the value at row V of VALS2 has a deleted instance.
[0241] Step 1C6, which is also done directly after step 1C2 if
value table row number V already has a deleted instance of its own,
sets J to a row number in column C of the instance table that is
associated with value table row number V. If column C of DISP
exists, J DISP[V,C] is such an instance. If DISP has no column C,
J=V is such an instance.
[0242] Step IC7 then finds the first deleted instance, K, which is
at one plus the row number returned by top_undel(C,J) (i.e.,
K=top_undel(C,J)+1). Step 1C8 then tests whether the previous
column, prev(C), is V/O split. If it is not, step 1C9 sets
VO.chainO[(prev(C)] to K. Otherwise, step IC10 sets
VO.chainO[(prev(C))] to K-DISP[V',C]-X, where V'=V and X=0 if DISP
is "first row number" format, or V'=V1 and X=1 if DISP is "last row
number" format. In either case, processing is then complete.
Record Deletion
[0243] Record deletion is performed in this embodiment by
identifying the pointer table cells of the record and marking them
as deleted in the DELS column when it exists, or by a tombstoning
flag. Such free space is then available for use when the data in
existing records is changed or new records are added. In unsorted
columns that are "attached" as described above, the delete status
of a cell in the attached column is identical to that of the cell
to which it is attached.
[0244] Deletion of a record is illustrated in FIG. 19. In step DR1,
the record to be deleted (the one containing cell [R0, C0]) is
loaded into ChainVO object VO. If the pointer chain starting from
[R0, C0] does not form a closed loop, an exception is raised,
terminating processing. Step DR2 determines whether the record has
any deleted cells (by, e.g., repeated testing of whether top_undel(
) returns a row number less than the cell's row number), because
only a live record can be deleted. If the record contains a deleted
cell, step DR3 reports an error and processing is complete. If no
cells in the record are deleted, step DR4 is performed, which
initializes the current column, C, to column C0 and the current
column, R, to R0. Step DR5 then deletes the current cell, [R, C],
and sets R to the row number in next(C), via a call to "Delete
pointer(s) cell [R,C]," described above. Step DR6 then sets C to
the next column via a call to next(C). If the current column is not
equal to the starting column (C not equal to C0), step DR7 loops
back to step DR5; otherwise, step DR7 terminates processing.
[0245] For example, if record "Five" is deleted in the example
above, all cells in INST (and possibly OCCUR) belonging to this
record will be marked as "deleted" (by tombstones for columns not
having DISP/DELS, and by the DELS column where it exists). For the
above example the DELS table will look as follows (if record "Five"
is the only one that has been deleted):
TABLE-US-00031 DELETES Row # ENGLISH SPANISH GERMAN TYPE PARITY 1 0
0 2 0 1 3 1 4 0 5 6
[0246] A count of records with, for example, TYPE="Prime" is now
obtained from column TYPE of DISP as 6-3 (difference of row 4 entry
and row 3 entry), indicating that there are three such records;
however, the DELETES structure indicates that one of those records
is deleted, hence the true total is 6-3-1=2. The number of records
with PARITY="Odd" is obtained similarly. DISP shows the value 4 in
row 2 of the PARITY column. Hence, rows 4 through 6 (last row) of
INST are associated with "Odd", three records in all. Again, there
is a "1" in the PARITY column of DELETES, row 2, so the number of
undeleted records with PARITY="Odd" is 3-1=2.
Record Insertion
[0247] Insertion of a new record is illustrated in FIG. 20. Step
IRI obtains the values for the new record's fields (for example,
from a user) and stores them in a temporary buffer. A ChainVO
object VO is also allocated for record construction and insertion.
Fields belonging to an "attached" column, as described above, are
treated essentially as suffixes to the values in the column to
which they are attached. Step IR2 sets the current column C to the
first column. Step IR3 then searches the value table, VALS2, for
the value, V, specified as the new record's column C value, and
returns the sort position, V, of the value and whether the value
already exists. Note that when prev(C) is V/O split, the search in
VALS2 is done in two parts; first, the original, sorted value list
is searched and then, if no match is found, the appended listed of
added values is searched through the permutation list (as described
above). Step IR4 tests whether the value already exists. If it
does, step IR8 is executed; otherwise step IR5 is executed.
[0248] Step IR5 determines whether column C is V/O split (in which
case the column descriptors for prev(C) of the instance table would
indicate V/O splitting). If it is V/O split, step IR7 is performed,
which inserts the new value into VALS2, DISP, and DELS via a call
to insert_vov(V,C,*new value). If it is not V/O split, step IR6 is
performed, which inserts the new value int VALS2, DISP, and DELS
via a call to insert_v(V,C,*new value).
[0249] In either case, step IR8 then builds chainV in the VO
object, setting VO.chainV[prev(C)]=V, where V is either the sort
position found in step IR3 (if column prev(C) is not V/O split), or
h_val found in "insert ovo" (if column prev(C) of the instance
table is V/O split).
[0250] Step IR9 determines whether the value at row V of VALS2 has
deleted instances (by checking the DELS table column if it exists,
otherwise by counting tombstones). If it does not, step IR10 is
performed, which provides a deleted instance for the value via a
call to insert_c(VO,C) (updating VO.chainO[prev(C)] in the
process).
[0251] If there is already a deleted instance, the branch starting
with step IR11 is performed. In step IR11, the row number, K, in
the instance table of the first deleted instance is found via a
call to top_undel(C,J)+1, where J represents the row number, in
column C of the instance table, of an instance of value number V.
In particular, if column C of DISP exists, then J=DISP[V,C] is such
an instance. In the absence of column C of DISP, J=V is such an
instance. Step IR12 then determines whether column prev(C) of the
instance table is V/O split. If prev(C) is V/O split, then step IRI
3 sets VO.chainO[prev(C)] to the appropriate occurrence number,
i.e., K-DISP[V',C]-X, where V'=V and X=0 if DISP is in "first row
number" format, or V'=V 1 and X=1 if DISP is "last row number"
format). If prev(C) is not V/O split, step IR14 loads the row
number of the deleted instance, K, into VO.chainO[prev(C)].
[0252] In either case, step IR15 then deducts the deleted instance
from the deletes count for row V of VALS2. Step IR16 then moves on
to the next column, setting C to next(C). Step IR 7 then determines
whether all columns have been processed (i.e., whether C equals
column 0) and, if not, loops back to step IR3. Otherwise, step IR18
writes the whole object VO back into the instance table (via a call
to put_chain(0, VO, fcount), where fcount is the number of fields
in the record), and processing is complete.
Record Updates
[0253] Updating an existing record is illustrated in FIG. 21. In
step E1, the user chooses a record to be updated and, in step E2,
the record is loaded into a ChainVO object VO and in a temporary
buffer. Any cell of the record may be selected as a starting point
for loading VO. In step E3, the user optionally changes any or all
field values (unless read-only conditions pertain) in the temporary
buffer. Step E4 initializes the "current column," C, to start at
the first column, column 0. Step E5 determines whether the user
changed the value in field/column C. If the user has not changed
the value, no processing is needed in this column, and step E20 is
performed, which advances C to the next column, by setting C to
next(C).
[0254] If the column C value has changed, step E6 is performed,
which deletes the formerly live instance of the record's old value,
via a call to "Delete pointer(s) cell [R,C]", described above. Step
E7 then searches the value table (using, e.g., a binary search) for
the value specified as the new record's column C value, and returns
the sort position of the value, whether matched or not. When
prev(C) is V/O split, the search of the value table is done in two
parts; first, the original, sorted value list is searched and then,
if no match is found, the appended listed of added values is
searched through the permutation list (as described above). Step E8
tests whether the new value was already in VALS2. If it was, the
branch starting with step E12 is performed; otherwise the branch
starting with step E9 is performed.
[0255] Step E9 determines whether the column prev(C) is V/O split.
If it is V/O split, step E11 inserts the new value into VALS2,
DISP, and DELS via a call to insert_vov(V,C,*new value); otherwise,
step E10 inserts the new value via a call to insert_v(V,C,*new
value). Step E12 builds the chainV of the new record, one element
at each pass, setting VO.chainV[prev(C)]=V, where V is either the
sort position found in step E7, if column prev(C) is not V/O split,
or h_val found in "insert_vov( )," if column prev(C) is V/O split.
Step E13 determines whether the value at row V has deleted
instances by looking in the DELS table, or counting tombstones if
DELS has no corresponding column. If the value has no deleted
instances, the branch starting at step E14 is executed. Step E14
provides a deleted instance for the value, via a call to
insert_c(VO,C), and updates VO.chainO[prev(C)] in the process.
Otherwise, the branch starting at step E15 is executed. Step E15
finds the row number, K, in column C of the first deleted instance
of value number V; i.e., K=top_undel(C,J)+1, where J represents the
row number, in column C of the instance table, of an instance of
value number V. In particular, if column C of DISP exists, then
J=DISP[V,C] is such an instance; otherwise, J=V is such an
instance. Step E16 tests whether column prev(C) is V/O split. If it
is V/O split, then step E18 is performed, which sets K to the
occurrence number; i.e., K=K-DISP[V',C]-X, where V'=V and X=0 if
DISP is "first row number" format, or V'=V1 and X=1 if DISP is
"last row number" format. In either case, step E17 is then
performed, which loads the proper data into VO.chainO; i.e.,
VO.chainO[prev(C)]=K. Step E19 then removes the deleted instance
from the deletes count. Step E20 then changes C to the next column
(C=next(C)). Step E21 tests whether all columns have been
processed; i.e., whether C=0, which was the starting column. If C
has not returned to the starting column, execution loops back to
step E5 and repeats with the new C value. Otherwise, step E22
writes the whole object VO back into the instance table, via a call
to put_chain(O, VO, fcount), and processing is done.
Queries
[0256] Because columns in the database system of the present
invention may be independently sorted, queries can be performed
very quickly. Any of a variety of efficient, standard search or
lookup algorithms can be used. For example, a simple binary search
delivers a worst case time performance of C log2 n, and an average
performance of C log2 (n/2). Other search techniques can also be
used, with the best one being dependent on the specific situation
and characteristics of the data.
[0257] Parallelization can be implemented on top of either a binary
midpoint or interpolation search. Such techniques for
parallelization of search algorithms are known in the art. Further
parallelization can be obtained by grouping rows of sorted data
elements from each column in size n containers, where n equals
either the number of processors or an integral multiple thereof.
The system tracks the upper and lower boundary points of these
containers, removing the necessity of data being sorted within
them. Where n equals the number of processors, entire containers
can then be searched and manipulated with the same efficiency that
single rows are operated upon in single processor environments,
while displacements within these containers become
inconsequential.
[0258] As an example, a flowchart for a query for all records
having a chosen value for a given field is illustrated in FIG. 22.
In step 221, the value table for a particular field is searched for
the values matching the chosen value, M. Again, because the columns
are generally in sorted order, a binary search can be used (as well
as other search techniques). Step 222 tests whether a matching
value was found. If a matching value is not found, that is reported
in step 223.
[0259] If a matching value is found, for example at Value_Table(r,
c), steps 224 and 225 are performed, which determine the row in the
value table with matching values (step 224) and reconstruct the
records associated those rows (step 225). For a non-condensed
column, the record associated with the cell with the matching value
is reconstructed as discussed above; then contiguous rows (r+1,
r+2, . . . , r-1, r-2, . . . ) are checked for matching values, and
if additional matching values are found the records associated with
those cells are also reconstructed. The search of contiguous rows
can stop in any direction when a non-matching value is found.
[0260] For a condensed column, the range of instance table row
numbers that point to the matching value is obtained from the
displacement table. Again, where the matching value was found at
Value_Table(r, c), the contents of Displacement_Table(r, c), if in
"first row number" format, is the beginning of the range and
Displacement_Table(r+1, c)-1 is the end of the range (unless r is
the last row in the displacement table, in which case the end of
the range is the last row in the instance table for the column).
Step 225 then reconstructs, as described above, the records
containing the cells identified in the instance table.
[0261] More complicated queries, such as (FIELD_X=M).AND.
(FIELD_Y=N), (FIELD_X=M) OR. (FIELD_Y=N), and so on, are also
efficiently implemented using the data structures described herein.
For example, an AND query can be implemented by finding (as above)
all records matching FIELD_X=M, then testing for the second
condition (e.g., FIELD_Y=N) during record reconstruction.
[0262] A significant advantage of the present invention is that the
AND condition query can be performed with fewer steps because, for
condensed columns, the number of rows meeting each of the
conditions is already known from the displacement table. The first
condition to be applied can then be chosen to be the one with fewer
matches. In contrast, existing database engines typically must
perform "analysis" cycles periodically in order to have only an
approximate idea of the cardinality found in each column. With the
embodiments of the present invention described above, the
cardinalities are known ahead of time for each value. An OR query
can be implemented, for example, by finding all records matching
the first condition and then finding all records matching the
second condition that were not already matched by the first
condition. If an arbitrarily complex expression is known in advance
to be a frequent query, a sorted column for that expression can be
included in the value, displacement and instance tables just as
though it were an ordinary field, and the same rapid binary search
method would apply.
[0263] Data structures, corresponding to those discussed above, can
be initialized with the results of a query, thus facilitating
sub-queries.
SQL Functions
[0264] Many SQL functions may be supported by the data structures
in accordance with the present invention with a trivial amount of
computational effort. For example, the COUNT function, which
returns the number of records having a specified value for a given
attribute, is available in constant time by accessing the entries
for that value and the adjacent value in the displacement table.
The MAX and MIN functions, which find the records with the maximum
and minimum values for a given attribute, can be implemented by
accessing the top and bottom cells, respectively, in the given
column. The MEDIAN function, which finds the record with the middle
value for a given attribute, can be implemented by searching for
the location of the displacement table closest to half the record
count, and returning the associated value. The MODE function, which
finds the value with the largest number of occurrences, can be
implemented by a linear search for the largest difference in
adjacent displacement table values, and using the corresponding
value. These functions (called aggregation functions) are efficient
because the displacement table is directly related to the histogram
of value counts within the column.
[0265] INSERT, DELETE, and UPDATE operations are supported as
shown, for example, in the embodiments of these operations
described above.
[0266] The present invention also supports other types of SQL
queries. For example, suppose there are two tables, labeled "PLANT"
and "EMPLOYEE", whose various attributes are shown below:
[0267] PLANT:
[0268] PLANT_NAME PLANT_NUMBER MANAGER_ID etc. . . .
[0269] EMPLOYEE:
[0270] EMPLOYEE_NAME EMPLOYEE_ID JOB ADDRESS etc. . . .
[0271] A query, for example, to find the name of each manager of
each plant is expressed in SQL as follows:
TABLE-US-00032 SELECT EMPLOYEE_NAME FROM PLANT, EMPLOYEE WHERE
MANAGER_ID = EMPLOYEE_ID
[0272] If the representations for the two tables are uncoupled,
i.e., they each have separate value, instance, displacement, and
occurrence tables, simple nested loops can be used to test for
equality between values in the MANAGER_ID column of the PLANT
database and the EMPLOYEE_ID column of the EMPLOYEE database, and,
for each match, the corresponding EMPLOYEE_NAME in the EMPLOYEE
database can be found.
[0273] If the instance, displacement, and occurrence tables of the
EMPLOYEE and PLANT databases point to the same value table with a
single MANAGER_ID/EMPLOYEE_ID column, then, for each displacement
table that has an entry for a particular column for both EMPLOYEE
and PLANT, the corresponding EMPLOYEE_NAME in the EMPLOYEE table
can be found.
Joins
[0274] A join operation combines two or more tables to create a
single joined table. For example, two tables may each have
information about EMPLOYEES and a join might be performed to
determine all information in both tables about each EMPLOYEE.
[0275] In order to perform a join, tables are typically linked
through a primary or candidate key in one of the tables. The
primary or candidate key is an attribute or attribute combination
that is unique. A redundant representation of this same attribute
or attribute combination, called a foreign key, is contained in one
or more other tables. The foreign keys need not have the same
cardinality as the primary or candidate key and need not be
unique.
[0276] A join operation is defined as a subset of an extended
Cartesian product of two or more tables. A Cartesian product of two
record-based tables combines each row of the first table with every
row of the second table. For example, if the first table had M rows
and N columns and the second table had P rows and Q columns, the
Cartesian production would have M.times.P rows and N+Q columns. An
extended Cartesian product is a Cartesian product that results from
inserting null values into one or more of the original tables.
[0277] A membership function defines the subset of the extended
Cartesian product of two or more tables that are in the join answer
set (i.e., the output of the join operation). The membership
function contains a comparison condition and a join criterion that
jointly determine a particular join type, which together with
column selectors determine the answer set returned by the join.
[0278] The comparison condition specifies a logical operator. It
is, for example, what appears between the attribute names in the
"Where" clause of an SQL SELECT statement. The most common
comparison condition is equality and the corresponding join is
referred to as an equi-join. Other conditions such as greater than
or less than are also possible.
[0279] The join criterion specifies the answer set of a join, given
a comparison condition, specific join attributes and column
selectors. For convenience equi-joins on a single attribute in each
table are assumed in the discussion below. Join criteria include
inner join (the join answer set consists of those rows that appear
in both tables), outer join (further subdivided into left outer
join, right outer join and full outer join--the join answer set
consists of all the rows in the left, right or either table
together with the corresponding rows of the other table where they
exist, null filled otherwise), union join (the join answer set
consists of those rows that appear in only one of the two tables,
with the remaining values in those rows null filled), and cross
join (the join answer set consists of the full non-extended
Cartesian product of the two tables).
[0280] The column selectors specify which columns are returned in
the answer set of the join.
[0281] In prior art database systems, joins tend to be extremely
costly in storage space and/or processing time, requiring either
pre-indexed data to maintain sortedness or a time intensive search
involving multiple passes over the entirety of each attribute that
is being joined. In the latter case, the time to do a two column
join is proportional to the square of the number of rows, a
three-column join proportional to the cube, etc., for tables of
equal cardinality and equal to the n-fold product of record counts
otherwise.
[0282] The present invention largely eliminates the overhead
associated with joins. All attributes can be sorted, and union
columns can eliminate the need to maintain redundant copies of
data. Membership functions can be implemented efficiently through
the displacement table, various alternate displacement tables, bit
maps, and/or n-valued logic functions.
Alternate Displacement Tables
[0283] Certain properties of the union column lead to various
modifications to the displacement table columns, which are
particularly useful in performing joins. The "full" displacement
structure has, for each column, rows that are in one-to-one
correspondence with the rows of the corresponding column of the
(condensed) value table. The contents of a cell of the full
displacement table, in one embodiment, is the row number of the
first (or last, depending on the embodiment) instance in the
instance table of all instances possessing the corresponding value
in the value table. If a value in the value table has no instances
at all, identical entries in the displacement table in the
corresponding and next (alternatively, previous) cells will
indicate this. Consequently, if there are many more values without
than with instances (referred to hereafter as the "sparse" case),
there are many more repeated than different values in the
displacement structure, leading to redundancy in the displacement
table. In the full displacement table, in one embodiment, the
entries are in sorted order, so that for row number J in the
instance table, the corresponding row number V in the value table
is that for which DISP[V,I]<=J<DISP[V+1,I] (for a
displacement column in the "first row number" format), or (for
"last row number format) DISP[V-1,I]<J<=DISP[V,I].
[0284] In a "sparse" case, an alternative format for displacement
table column(s) (referred to below as the "condensed" displacement
format) can be used to remove redundancy. In this format,
displacement table entries have two parts:
[0285] 1) DV, the row number in the value table of a value having
instances, and
[0286] 2) DD, the starting (alternately, ending) row number in the
instance table of the actual instances of the value.
[0287] The row number entries DD are in sorted order; DV will
naturally also be in sort order when the underlying value table is
in sort order.
[0288] For row number J in column I of the instance table, the
corresponding row number V in the value table is found as
follows:
[0289] 1) find K, via, e.g., a binary search, such that
DD[K]<=J<DD[K+1] (for "first row number" format) or (for
"last row number format") DD[K-1]<J<=DD[K];
[0290] 2) V=DV[K].
[0291] A condensed displacement column, when appropriate,
simultaneously saves storage space and speeds up binary searching.
However, testing for the presence of instances of a given value is
a constant-time lookup using a full displacement column, but a log
time binary search using a condensed displacement column.
[0292] In the case where values without instances are rare, a
further alternate format of the displacement table (referred to
herein as "dense" format) permits all missing values to be found
quickly. In this alternate format, displacement table entries have
a bitflag to identify values with no instances, and, for those
values with no instances, the contents of the entry is a pointer to
the next value without instances. (The originally defined
displacement list, lacking the linked list of missing values, is
referred to below as "full" format).
Examples of Alternate Displacement Tables
[0293] Sparse and dense displacement columns are illustrated below
for prior art, record-type, tables J.sub.mod and SPJ.sub.mod
(excerpted from C. J. Date, Introduction to Database Systems, Sixth
Edition, inside front cover (1995)):
[0294] J.sub.mod:
TABLE-US-00033 Rec # J# JNAME CITY 0000: J1 Sorter Paris 0001: J3
OCR Athens 0002: J4 Console Athens 0003: J5 RAID London 0004: J6
EDS Oslo
[0295] SPJ.sub.mod:
TABLE-US-00034 Rec # S# P# J# QTY 0000: S2 P3 J2 200 0001: S2 P3 J5
600 0002: S2 P5 J2 100 0003: S3 P4 J2 500 0004: S5 P2 J2 200 0005:
S5 P5 J5 500 0006: S5 P6 J2 200
[0296] Value, displacement, instance and occurrence tables for
J.sub.mod and SPJ.sub.mod are as follows:
[0297] J.sub.mod:
[0298] VALS:
TABLE-US-00035 Row # J# JNAME CITY 0000 J1 Console Athens 0001 J3
EDS London 0002 J4 OCR Oslo 0003 J5 RAID Paris 0004 J6 Sorter
[0299] DISP:
TABLE-US-00036 Row # J# JNAME CITY 0000 0 0 0 0001 1 1 2 0002 2 2 3
0003 3 3 4 0004 4 4
[0300] Combined Instance/Occurrence Table:
TABLE-US-00037 Row# J# JNAME CITY 0000 4/0 0/1 1/0 0001 2/0 2/0 2/0
0002 0/0 0/0 3/0 0003 3/0 1/0 4/0 0004 1/0 3/0 0/0
[0301] SPJ.sub.mod:
[0302] VALS:
TABLE-US-00038 Row # S# P# J# QTY 0000 S2 P2 J2 100 0001 S3 P3 J5
200 0002 S5 P4 500 0003 P5 600 0004 P6 0005 0006
[0303] DISP:
TABLE-US-00039 Row # S# P# J# QTY 0000 0 0 0 0 0001 3 1 5 1 0002 4
3 4 0003 4 6 0004 6 0005 0006
[0304] Instance/Occurrence Table:
TABLE-US-00040 Row # S# P# J# QTY 0000 1/0 0/2 0/0 0/2 0001 1/1 0/1
1/0 0/0 0002 3/0 1/1 1/1 2/0 0003 2/0 0/4 1/2 2/2 0004 0/0 0/0 2/0
1/0 0005 3/1 1/0 2/1 2/1 0006 4/0 0/3 3/0 0/1
[0305] To facilitate rapid join queries on, for example, over the
J# attribute of tables J.sub.mod and SPJ.sub.mod, a union column
for J# is created and sparse and dense displacement table columns
corresponding to the union column are incorporated into the
displacement tables for J.sub.mod and SPJ.sub.mod. The J# union
column for J.sub.mod and SPJ.sub.mod is as follows:
[0306] J# Union for J.sub.mod and SPJ.sub.mod:
TABLE-US-00041 Row # J# 0000 J1 0001 J2 0002 J3 0003 J4 0004 J5
0005 J6 0006 J7
[0307] The appropriate type of displacement column for each of
J.sub.mod and SPJ.sub.mod is determined by comparing the
cardinality of the union column to the cardinalities of the
corresponding columns of the J.sub.mod and SPJ.sub.mod tables. The
cardinality of the J# union column above is 7. The cardinality for
the J# column in the J.sub.mod table is 5. Since nearly all values
in the union column also appear in the J.sub.mod table, a dense
displacement column is constructed for that attribute. For the
SPJ.sub.mod table, the cardinality of its J# column, 2, is compared
to the cardinality of the union column, 7. Since the J# values are
"sparse" in this case, a sparse displacement column for the
SPJ.sub.mod column is constructed. The J# union column, the
displacement column for J.sub.mod and the displacement column for
SPJ.sub.mod are shown below, all in one table for illustration
purposes:
[0308] Union and Displacement Columns:
TABLE-US-00042 J.sub.mod SPJ.sub.mod Row # J# Union D-column
D-column 0000 J1 0 1/0 0001 J2 *6 4/5 0002 J3 1 0003 J4 2 0004 J5 3
0005 J6 4 0006 J7 *1
[0309] In the dense displacement column for J.sub.mod, the
asterisks are bitflags, indicating (1) that J.sub.mod does not have
a record with the corresponding value, and (2) that the value which
follows is a pointer to the next value in the union column which
does not appear in J.sub.mod. Those values in the union column
which do not appear in J.sub.mod are thus maintained in a circular
linked list.
[0310] In the sparse displacement column for SPJ.sub.mod, the
entries are presented in the format DV/DD, where DV is a pointer to
a value in the union column which has instances in the SPJ.sub.mod
table and the DD pointer is the starting row number in the
SPJ.sub.mod instance/occurrence table of the instances of the given
value.
Modelling Joins Using Bit Maps
[0311] The J# union column for the J.sub.mod and SPJ.sub.mod tables
may also be supplemented by bit maps. The bit map will indicate
whether a given value in the union column is contained in the
J.sub.mod or SPJ.sub.mod tables. A procedure for creating such a
structure is illustrated below. The bit map in this example
consists of seven entries, 0000 through 0006, one for each value of
J# present in the union column. Each entry is associated with 2
bits. The first bit is set to 1 if the corresponding value of J# is
present in the J.sub.mod table, 0 otherwise. Likewise, the second
entry is set to 1 if the J# value is present in the SPJ.sub.mod
table, and 0 otherwise.
[0312] Since the J.sub.mod table is represented by a dense
displacement column, its bit entries are initialized to `1` (since
almost all the values in the union column are contained in
J.sub.mod). Likewise, since SPJ.sub.mod is represented by a sparse
displacement column, its bit entries are initialized to `0` (since
few of the values in the union column are present in SPJ.sub.mod).
The initial bit map is thus as follows:
[0313] Initial Bit Map:
TABLE-US-00043 Row # J.sub.mod/SPJ.sub.mod 0000 1/0 0001 1/0 0002
1/0 0003 1/0 0004 1/0 0005 1/0 0006 1/0
[0314] The next step is to construct the final bit map. For the
J.sub.mod column, the values not present in the J# union column are
contained in the ring of non-present values in its dense
displacement column. The ring is traversed and the corresponding
entries in the bit map are set to `0`.
[0315] To correct the entries for the SPJ.sub.mod column, the DV
pointers point to the values in the union column which have entries
in the SPJ.sub.mod tables and the corresponding entries in the bit
map are set to `1`. The final bit map is as follows:
[0316] Final Bit Map:
TABLE-US-00044 Row # J.sub.mod/SPJ.sub.mod 0000 1/0 0001 0/1 0002
1/0 0003 1/0 0004 1/1 0005 1/0 0006 0/0
[0317] N-valued logic functions can model join operations with
functions over bit maps. This technique is illustrated by the
example below with reference to prior art tables S. P, and J (from
C. J. Date, Introduction to Database Systems, Sixth Edition, inside
front cover (1995)):
[0318] S:
TABLE-US-00045 S# SNAME STATUS CITY S1 Smith 20 London S2 Jones 10
Paris S3 Blake 30 Paris S4 Clark 20 London S5 Adams 30 Athens
[0319] P:
TABLE-US-00046 P# PNAME COLOR WEIGHT CITY P1 Nut Red 12 London P2
Bolt Green 17 Paris P3 Screw Blue 17 Rome P4 Screw Red 14 London P5
Cam Blue 12 Paris P6 Cog Red 19 London
[0320] J:
TABLE-US-00047 J# JNAME CITY J1 Sorter Paris J2 Display Rome J3 OCR
Athens J4 Console Athens J5 RAID London J6 EDS Oslo J7 Tape
London
[0321] In this example a union join is performed on the "CITY"
columns of the S, P, and J tables. This entails finding only those
records whose "CITY" value appears in exactly one of the S, P, or J
tables.
[0322] The first step is to construct a union column for the CITY
columns of S, P, and J, if one does not already exist.
[0323] The second step is to associate with each value of the union
column three bits, corresponding to the S, P, and J tables,
respectively. A bit is set to `Y` (i.e., `1`) if the CITY value is
present in the appropriate table, and to `N` (i.e., `0`) otherwise.
Such a table is depicted below:
[0324] Union Column and Bit Map:
TABLE-US-00048 CITY S P J Athens Y N Y London Y Y Y Oslo N N Y
Paris Y Y Y Rome N Y Y
[0325] For a particular value of the CITY attribute, records with
that value appear in the union join if and only if that value of
CITY appears in exactly one of the S, P, and J tables, i.e.,
exactly one of the bits in the bitmap for the union column equals
`Y`. One illustrative implementation of a function that finds such
rows is function f(temp, column) described below. The function's
domain consists of the two variables `temp` and `column`. The
variable `temp` can be one of three values; `Y`, `N`, or `D`. The
variable `column` is either `Y` or `N`. Lastly, the return value of
function f also consists of the three values `Y`, `N`, or `D`.
[0326] For each value of CITY in the union column, function f is
applied iteratively to the bit values in each of the three columns:
the variable `column` is set to the bit value of the current
column, and `temp` is assigned the result of the previous
application of the function f. For the first column, S, `temp` is
initialized to `N`. After the final iteration, if the result is
`Y`, the value appears in the union join; if the result is `N` or
`D`, the value does not appear.
[0327] The function f is defined as follows:
TABLE-US-00049 Temp Column Return Value N N N Y N Y D N D N Y Y Y Y
D D Y D
[0328] Applying this function to the first row in the Union Table,
corresponding to the value `Athens`, yields the following result:
f(f(f(`N`,`Y`),`N`),`Y`), which equals `D`. Hence `Athens`, which
appears twice in the row, does not appear in the Union Join.
Applying function f to the row for `Oslo` yields the following
result: f(f(f(`N`,`N`),`N`),`Y`), which equals `Y`. Hence `Oslo`,
which appears exactly once in the row, does appear in the union
join.
[0329] FIG. 23 is a flowchart that illustrates a join operation. In
step 231, the user picks tables to join. In step 232, any tables
not already represented in the data structures of the present
invention are converted into such structures. Next, in step 233,
columns, if any, are picked whose values are part of the logical
expression defining the join as a subset of the extended Cartesian
product. Step 234 tests if any columns were selected. If no columns
were selected, the join corresponds to the full non-extended
Cartesian product, and record reconstruction proceeds via step 238
without conditional constraints (i.e., every record from each table
is combined with every record of every other table).
[0330] Otherwise step 235 is performed which tests if more than one
column was selected. If so, those columns are combined into a
combined column (such as in the "combined columns" description
above).
[0331] If the appropriate value table union column does not already
exist, step 237 creates it, together with its associated
displacement table columns. Step 238 then modifies the ranges in
the routines that produce the join output, using full, dense and/or
sparse displacement lists, bitmaps, multivalued logic functions or
any combination of them, so as to match the type of join, using the
appropriate comparison condition and join criterion.
[0332] For example, the answer set of an inner join is limited to
instance table cells corresponding to displacement table rows in
which the tables involved have non-null record ranges. This can be
determined, for example, from their displacement table entries.
Corresponding instance cell entries derived from each such
displacement table row (and possibly one of the adjacent rows,
depending on the implementation) provide the instance table cell
ranges for each table for all matching records. The answer set is
restricted to only those records, producing the appropriate inner
join answer set. The answer sets for other types of joins can be
similarly determined from, for example, the displacement table.
[0333] Combination with the query methods discussed above enables
implementation of a full range of statements like SQL's "SELECT . .
. WHERE . . . "
[0334] While the invention has been particularly shown and
described with reference to particular illustrative embodiments
thereof, it will be understood by those skilled in the art that
various changes in form and details are within the scope of the
invention, which is defined by the claims.
* * * * *