Imported: 13 Feb '17 | Published: 18 Jan '11

USPTO - Utility Patents

Methods, computer programs, and database systems for performing a database query to join a column A and a column B on an inequality condition are disclosed. A database includes value-count indexes for columns A and B. Minimum and a maximum values for A and B are determined, using the value-count indexes for A and B, respectively. The method includes defining three or more sets of values in A and B, relative to the minimum and maximum values for B and A, respectively. The method includes generating one or more Cartesian products between values in A and B. The database query is performed on a set of values in A and a set of values in B to generate a partial query result. The method includes merging one or more Cartesian products and the partial query result.

This application is related to the United States Patent Application entitled Dynamic Partition Enhanced Joining by Mark Morris and Bhashyam Ramesh, Ser. No. 10/862,686, filed on even date.

This application is related to the United States Patent Application entitled Dynamic Partition Enhanced Joining Using A Value-Count Index by Mark Morris and Bhashyam Ramesh, Ser. No. 10/862,689, filed on even date.

One important feature in relational database system (RDBMS) is the ability to perform queries that join columns from two or more tables. An example of a query including a join is:

SELECT T**1**.*, T**2**.* FROM T**1**, T**2** WHERE T**1**.A equality_condition T**2**.B;

where T**1** and T**2** are tables, T**1**.A is a column in T**1**, T**2**.B is a column in T**2**, and equality_condition is any condition requiring equality between the operands to the condition. The example query above will return all of the columns in T**1** horizontally concatenated with all of the columns in T**2**, for rows where T**1**.A and T**2**.B satisfy the equality condition. In mathematical terms, this query may be described as a Cartesian product with a condition or cross product with a condition.

In general, in one aspect, the invention features a method of performing a database query to join a column A and a column B on an inequality condition. A database includes value-count indexes for columns A and B. The method includes determining a minimum and a maximum value for A, using the value-count index for A. The method includes determining a minimum and a maximum value for B, using the value-count index for B. The method includes defining three or more sets of values in A, relative to the minimum and maximum values for B. The method includes defining three or more sets of values in B, relative to the minimum and maximum values for A. The method includes generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B. The method includes performing the database query on a set of values in A and a set of values in B to generate a partial query result. The method includes merging one or more Cartesian products and the partial query result.

Implementations of the invention may include one or more of the following. Determining a minimum and a maximum value for A, using the value-count index for A may include scanning the value-count index for A to determine the minimum value for A and the maximum value for A. Determining a minimum and a maximum value for B, using the value-count index for B may include scanning the value-count index for B to determine the minimum value for B and the maximum value for B.

Column A may be in a table T**1** that includes zero or more rows and one or more columns. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if A is less than the minimum value for B, projecting one or more columns from the row into a partition D. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, projecting one or more columns from the row into a partition E. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if A is greater than the maximum value for B, projecting one or more columns from the row into a partition F.

Column B may be in a table T**2** that includes zero or more rows and one or more columns. Defining three sets of values in B, relative to the minimum and maximum values for A may includes, for each row in T**2**, if B is less than the minimum value for A, projecting one or more columns from the row into a partition X. Defining three sets of values in B, relative to the minimum and maximum values for A may includes, for each row in T**2**, if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y. Defining three sets of values in B, relative to the minimum and maximum values for A may includes, for each row in T**2**, if B is greater than the maximum value for A, projecting one or more columns from the row into a partition Z.

The inequality condition may be a “less than” or a “less than or equal” condition. Generating one or more Cartesian products may include generating a Cartesian products of partition D and partition Y, generating a Cartesian product of partition D and partition Z, and generating a Cartesian product of partition E and partition Z. Performing the database query on a set of values in A and a set of values in B to generate a partial query result may include performing the database query on partition E and partition Y. Merging one or more Cartesian products and the partial query result may include merging one or more of the following: the partial query result of the database query on partition E and partition Y, the Cartesians product of partition D and partition Y, the Cartesian product of partition D and partition Z; and the Cartesian product of partition E and partition Z.

The inequality condition may be a “not equal” condition. Generating one or more Cartesian products may include generating one or more of the following Cartesian products: the Cartesian product of partition D and partition Y, the Cartesian product of partition D and partition Z, the Cartesian product of partition E and partition X, the Cartesian product of partition E and partition Z, the Cartesian product of partition F and partition X; and the a Cartesian product of partition F and partition Y. Performing the database query on a set of values in A and a set of values in B to generate a partial query result may include performing the database query on partition E and partition Y. Merging one or more Cartesian products and the partial query result may include merging one or more of the following: the partial query result of the database query on partition E and partition Y, the Cartesian product of partition D and partition Y, the Cartesian product of partition D and partition Z, the Cartesian product of partition E and partition X, the Cartesian product of partition E and partition Z, the Cartesian product of partition F and partition X; and the Cartesian product of partition F and partition Y.

Generating one or more Cartesian products may include merging partition D and partition F to form a partition DF. Generating one or more Cartesian products may include merging partition X, partition Y, and partition Z to for a partition XYZ. Generating one or more Cartesian products may include generating a Cartesian product of partition DF and partition XYZ. Performing the database query on a set of values in A and a set of values in B to generate a partial query result may include performing the database query on partition E and partition Y. Merging one or more Cartesian products and the partial query result may include merging one or more of the following: the partial query result of the database query on partition E and partition Y; the Cartesian product of partition DF and partition XYZ; the Cartesian product of partition E and partition X; and the Cartesian product of partition E and partition Z.

The inequality condition may be a “not equal” condition. Performing the database query on a set of values in A and a set of values in B to generate a partial query result may include performing the database query on partition E and partition Y.

The inequality condition may be a “less than or equal” condition or a “greater than or equal” condition. Column A may be in a table T**1** that includes zero or more rows and one or more columns. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if T**1**.A is less than or equal to the minimum value for B, projecting one or more columns from the row into a partition D. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, projecting one or more columns from the row into a partition E. Defining three sets of values in A, relative to the minimum and maximum values for B may include, for each row in T**1**, if T**1**.A is greater than or the maximum value for B, projecting one or more columns from the row into a partition F.

Column B may be in a table T**2** that may include zero or more rows and one or more columns. Defining three sets of values in B, relative to the minimum and maximum values for A may include, for each row in T**2**, if T**2**.B is less than the minimum value for A, projecting one or more columns from the row into a partition X. Defining three sets of values in B, relative to the minimum and maximum values for A may include, for each row in T**2**, if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y. Defining three sets of values in B, relative to the minimum and maximum values for A may include, for each row in T**2**, if T**2**.B is greater than or equal to the maximum value for A, projecting one or more columns from the row into a partition Z.

The inequality condition may be a “greater than” condition. The method may include converting the query to a query including a “less than” inequality condition. The inequality condition may be a “greater than or equal to” condition. The method may include converting the query to a query including a “less than or equal to” inequality condition.

In general, in another aspect, the invention features a computer program, stored on a tangible storage medium for use in performing a database query to join a column A and a column B on an inequality condition. A database includes value-count indexes for columns A and B. The computer program includes executable instructions that cause a computer to determine a minimum and a maximum value for A, using the value-count index for A. The computer program includes executable instructions that cause a computer to determine a minimum and a maximum value for B, using the value-count index for B. The computer program includes executable instructions that cause a computer to define three or more sets of values in A, relative to the minimum and maximum values for B. The computer program includes executable instructions that cause a computer to define three or more sets of values in B, relative to the minimum and maximum values for A. The computer program includes executable instructions that cause a computer to generate one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B. The computer program includes executable instructions that cause a computer to perform the database query on a set of values in A and a set of values in B to generate a partial query result. The computer program includes executable instructions that cause a computer to merge one or more Cartesian products and the result.

In general, in another aspect, the invention features a database system that includes a massively parallel processing system. The massively parallel processing system includes one or more nodes, a plurality of CPUs, a plurality of data storage facilities, and a process for execution on the massively parallel processing system for performing a database query to join a column A and a column B on an inequality condition, a database including value-count indexes for columns A and B. Each of the one or more nodes provide access to one or more CPUs. Each of the one or more CPUs provide access to one or more data storage facilities. The database includes value-count indexes for columns A and B. The process includes determining a minimum and a maximum value for A, using the value-count index for A. The process includes determining a minimum and a maximum value for B, using the value-count index for B. The process includes defining three or more sets of values in A, relative to the minimum and maximum values for B. The process includes defining three or more sets of values in B, relative to the minimum and maximum values for A. The process includes generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B. The process includes performing the database query on a set of values in A and a set of values in B to generate a partial query result. The process includes merging one or more Cartesian products and the result.

The techniques for performing joins disclosed herein have particular application, but are not limited, to large databases that might contain many millions or billions of records managed by a database system (“DBS”) **100**, such as a Teradata Active Data Warehousing System available from NCR Corporation. FIG. 1 shows a sample architecture for one node **105**_{1 }of the DBS **100**. The DBS node **105**_{1 }includes one or more processing modules **110**_{1 . . . N}, connected by a network **115**, that manage the storage and retrieval of data in data-storage facilities **120**_{1 . . . N}. Each of the processing modules **110**_{1 . . . N }may be one or more physical processors or each may be a virtual processor, with one or more virtual processors running on one or more physical processors.

For the case in which one or more virtual processors are running on a single physical processor, the single physical processor swaps between the set of N virtual processors.

For the case in which N virtual processors are running on an M-processor node, the node's operating system schedules the N virtual processors to run on its set of M physical processors. If there are 4 virtual processors and 4 physical processors, then typically each virtual processor would run on its own physical processor. If there are 8 virtual processors and 4 physical processors, the operating system would schedule the 8 virtual processors against the 4 physical processors, in which case swapping of the virtual processors would occur.

Each of the processing modules **110**_{1 . . . N }manages a portion of a database that is stored in a corresponding one of the data-storage facilities **120**_{1 . . . N}. Each of the data-storage facilities **120**_{1 . . . N }includes one or more disk drives. The DBS may include multiple nodes **105**_{2 . . . O }in addition to the illustrated node **105**_{1}, connected by extending the network **115**.

The system stores data in one or more tables in the data-storage facilities **120**_{1 . . . N}. The rows **125**_{1 . . . Z }of the tables are stored across multiple data-storage facilities **120**_{1 . . . N }to ensure that the system workload is distributed evenly across the processing modules **110**_{1 . . . N}. A parsing engine **130** organizes the storage of data and the distribution of table rows **125**_{1 . . . Z }among the processing modules **110**_{1 . . . N}. The parsing engine **130** also coordinates the retrieval of data from the data-storage facilities **120**_{1 . . . N }in response to queries received from a user at a mainframe **135** or a client computer **140**. The DBS **100** usually receives queries and commands to build tables in a standard format, such as SQL.

In one implementation, the rows **125**_{1 . . . Z }are distributed across the data-storage facilities **120**_{1 . . . N }by the parsing engine **130** in accordance with their primary index. The primary index defines the columns of the rows that are used for calculating a hash value. The function that produces the hash value from the values in the columns specified by the primary index is called the hash function. Some portion, possibly the entirety, of the hash value is designated a “hash bucket.” The hash buckets are assigned to data-storage facilities **120**_{1 . . . N }and associated processing modules **110**_{1 . . . N }by a hash bucket map. The characteristics of the columns chosen for the primary index determine how evenly the rows are distributed.

In one example system, the parsing engine **130** is made up of three components: a session control **200**, a parser **205**, and a dispatcher **210**, as shown in FIG. 2. The session control **200** provides the logon and logoff function. It accepts a request for authorization to access the database, verifies it, and then either allows or disallows the access.

Once the session control **200** allows a session to begin, a user may submit a SQL query, which is routed to the parser **205**. As illustrated in FIG. 3, the parser **205** interprets the SQL query (block **300**), checks it for proper SQL syntax (block **305**), evaluates it semantically (block **310**), and consults a data dictionary to ensure that all of the objects specified in the SQL query actually exist and that the user has the authority to perform the request (block **315**). Finally, the parser **205** runs an optimizer (block **320**), which develops the least expensive plan to perform the request.

An example system for performing a SQL query including one or more joins is shown in FIG. 4. The system starts and enters a loop defined by blocks **405** and **410**. The system will loop once for each join in the SQL query (block **405**). For example, assume the system receives the following SQL query:

SELECT T**1**.*, T**2**.*, T**3**.* FROM T**1**, T**2**, T**3** WHERE T**1**.A condition) T**2**.B AND T**1**.A condition**2** T**3**.C;

where T**1**, T**2**, and T**3** are tables, T**1**.A is a column in T**1**, T**2**.B is a column in T**2**, T**3**.**0** is a column in T**3**, and condition is a comparison between the operands to the condition. In one example implementation, the system will first perform a join between T**1** and T**2** on the condition T**1**.A condition) T**2**.B. Next, the system will perform a join between T**1** and T**3** on the condition T**1**.A condition**2** T**3**.C. Finally, the system will perform a join of the two previous results. In this example implementation, the query is decomposed into three join operations and the system will loop (block **405** and **410**) three times.

Another example system for performing a SQL query including one or more joins performs the example SQL query above using two joins. The system performs a join between T**1** and T**2** on the condition T**1**.A equality_condition T**2**.B and stores the result. In one example implementation, the result is stored in a work table or a spool table **51**. The system then performs a join between T**3** and S**1** on the condition S**1**.A equality_condition T**3**.C.

Within the loop defined by blocks **405** and **410** the system determines if the DBS **100** includes a Value Count Index (VCI) for each of the join columns (e.g., T**1**.A and T**2**.B). A VCI is a mechanism or data structure for tracking which values appear in a column and how many times the values appear in the column. One example VCI is an aggregate join index that is automatically updated each time a value in indexed column is added, deleted, or altered. The VCI typically contains two columns: a value column and a count column. The value column represents the value in the indexed column and the count column represents the number of occurrences of the value in the column. An example SQL query to create a value count index on T**1**.A is:

CREATE JOIN INDEX VCI**1***a *as SELECT A, COUNT(A) FROM T**1**;

If the DBS **100** does not include a VCI for each of the columns in the join (block **415**), the system evaluates other join methods (block **420**). Otherwise, the system determines if the join condition is a not equal join condition (i.e., “< >”), a less than join condition (i.e., “<”), or a less than or equal to join condition (i.e., “<=”) and, if so, the system processes the join (block **440**, which is described in greater detail below). Otherwise, the system determines if the join condition is a greater than join condition (i.e., “>”) or a greater than or equal to join condition (i.e., “>=”) and, if so the system converts the join to a less than or a less than or equal to join condition (block **435**, which is discussed in greater detail below). If the join condition is not an inequality condition, the system uses another join method (block **420**).

The system converts greater than and greater than or equal to conditions to less than and less than or equal to conditions (block **435**). One example system reverses the tables in the FROM clause and in the join condition and reverses the join condition operator. For example, the system converts conditions of the form:

SELECT T**1**.*, T**2**.* FROM T**1**, T**2** WHERE T**1**.A>T**2**.B;

to:

SELECT T**1**.*, T**2**.* FROM T**2**, T**1** WHERE T**2**.B<T**1**.A;

and conditions of the form:

SELECT T**1**.*, T**2**.* FROM T**1**, T**2** WHERE T**1**.A >=T**2**.B;

to:

SELECT T**1**.*, T**2**.* FROM T**2**, T**1** WHERE T**2**.B<=T**1**.A.

An example system for processing a join (block **440**) is shown in FIG. 5. The system receives a join of the following form:

SELECT T**1**.*, T**2**.* from T**1**, T**2** WHERE T**1**.A inequality_condition T**2**.B;

where T**1** and T**2** are tables, T**1**.A is a column in T**1**, and T**2**.B is a column in T**2**, and inequality_condition is any comparison that evaluates the operands for an inequality. Although T**1** and T**2** have separate designations in this example, in some implementations they are the same table. Likewise, in some implementations, columns T**1**.A and T**2**.B are the same column. While this example query returns all columns from T**1** and T**2**, certain implementations return zero or more columns from each of tables T**1** and T**2**. The database system includes a VCI for T**1**.A (i.e., VCI**1**A) and a VCI for T**2**.B (i.e., VCI**2**B).

The system determines the minimum and maximum values in column T**1**.A (block **505**). An example system for determining the minimum and maximum values in column T**1**.A is shown in FIG. 6. The system scans VCI**1**A to determine the minimum value in T**1**.A and the maximum value in T**1**.A (block **605**). The system may scan one or more rows to determine the minimum and maximum values for T**1**.A or, if the VCI for T**1**.A is sorted, the system may only have to read two locations to determine the minimum and maximum values in T**1**.A.

Returning to FIG. 5, the system determines the minimum and maximum values for column T**2**.B (block **510**). An example system for determining the minimum and maximum values for column B is shown in FIG. 7. The system scans the value count index for T**2**.B (i.e., VCl**2**B) to determine the minimum value in T**2**.B and the maximum value in T**2**.B (block **605**). The system may scan one or more rows to determine the minimum and maximum values for T**2**.B or, if the VCI for T**2**.B is sorted, the system may only have to read two locations to determine the minimum and maximum values in T**2**.B.

Returning to FIG. 5, the system partitions T**1**.A (block **515**). An example system for partitioning T**1**.A is shown in FIG. 8. The system determines if the join condition is a less than or equal to join condition and, if so, the system partitions T**1**.A by proceeding to block **810**, otherwise it partitions T**1**.A by proceeding to block **815**.

An example system for partitioning T**1**, where the join condition is not a less than or equal to condition (block **810**) is shown in FIG. 10. The system starts and enters a loop defined by blocks **1005** and **1010**. The system loops once for each row in T**1** (block **1005**). Within the loop, if the value of T**1**.A is less than the minimum value of T**2**.B (block **1010**), the system places one or more columns of the row in a partition D (block **1020**). If the value of T**1**.A is less than or equal to the maximum value of T**2**.B and greater than or equal to the minimum value of T**2**.B (block **1025**), the system places one or more columns of the row in a partition E (block **1030**). If the value of T**1**.A is greater than the maximum value of T**2**.B (block **1035**), the system places one or more columns of the row in a partition F (block **1040**). In one example system, each of the partitions D, E, and F are stored in worktables. In another example system the partitions D, E, and F are stored in a table with a partitioned primary index.

An example system for partitioning T**1**.A, where the join condition is a less than or equal to condition (block **815**) is shown in FIG. 11. The system starts and enters a loop defined by blocks **1005** and **1010**. The system loops once for each row in T**1** (block **1005**). Within the loop, if the value of T**1**.A is less than or equal to the minimum value of T**2**.B (block **1010**), the system places one or more columns of the row in the partition D (block **1020**). If the value of T**1**.A is less than or equal to the maximum value of T**2**.B and greater than the minimum value of T**2**.B (block **1025**), the system places one or more columns of the row in the partition E (block **1030**). If the value of T**1**.A is greater than the maximum value of T**2**.B (block **1035**), the system places one or more columns of the row in the partition F (block **1040**). In one example system, each of the partitions D, E, and F are stored in worktables. In another example system the partitions D, E, and F are stored in a table with a partitioned primary index.

Returning to FIG. 5, the system partitions T**2**.B (block **520**). An example system for partitioning T**2**.B is shown in FIG. 9. The system determines if the join condition is not a less than or equal to join condition and, if so, the system partitions T**2**.B by proceeding to block **910**, otherwise it partitions T**1**.A by proceeding to block **915**.

An example system for partitioning T**2**.B, where the join condition is not a less than or equal to condition (block **910**) is shown in FIG. 12. The system starts and enters a loop defined by blocks **1205** and **1210**. The system loops once for each row in T**2** (block **1205**). Within the loop, if the value of T**2**.B is less than the minimum value of T**1**.A (block **1210**), the system places one or more columns of the row in a partition X (block **1220**). If the value of T**2**.B is less than or equal to the maximum value of T**1**.A and greater than or equal to the minimum value of T**1**.A (block **1225**), the system places one or more columns of the row in a partition Y (block **1230**). If the value of T**2**.B is greater than the maximum value of T**1**.A (block **1235**), the system places one or more columns of the row in a partition Z (block **1240**). In one example system, each of the partitions X, Y, and Z are stored in worktables. In another example system the partitions X, Y, and Z are stored in a table with a partitioned primary index.

An example system for partitioning T**2**.B, where the join condition is a less than or equal to condition (block **915**) is shown in FIG. 13. The system starts and enters a loop defined by blocks **1305** and **1310**. The system loops once for each row in T**2** (block **1305**). Within the loop, if the value of T**2**.B is less than the minimum value of T**1**.A (block **1310**), the system places one or more columns of the row in the partition X (block **1020**). If the value of T**2**.B in the row is less than the maximum value of T**1**.A and greater than or equal to the minimum value of T**1**.A (block **1325**), the system places one or more columns of the row in the partition Y (block **1330**). If the value of T**2**.B is greater than or equal to the maximum value of T**1**.A (block **1335**), the system places one or more columns of the row in the partition Z (block **1340**). In one example system, each of the partitions X, Y, and Z are stored in worktables. In another example system the partitions X, Y, and Z are stored in a table with a partitioned primary index.

FIG. 14 shows an example of partitioned tables containing T**1**.A and T**2**.B. FIG. 15 shows examples value distributions within the partitions D, E, F, X, Y, and Z. The cross-hatched partitions represent partitions that include one or more values, while the unshaded partitions are empty. Because of the relationships between the partitions, some example systems do not determine the Cartesian product of certain combinations of partition. For example, one example system will not determine the Cartesian product of partitions D and X, because one of the partitions is empty. Another example system does not determine the Cartesian product of F and Z, because one of the partitions is empty.

Returning to FIG. 5, the system generates Cartesian products of the partitions (block **525**). An example system for generating Cartesian products is shown in FIG. 16. The system starts and determines if the join condition is a not-equal condition (i.e., “< >”) (block **1605**).

If the join condition is not a not equal condition (block **1605**), the system generates a Cartesian product of partitions D and Y and places the result in worktable DY. The system generates a Cartesian product of partitions D and Z and places the result in worktable DZ (block **1615**). The system generates a Cartesian product of partitions E and Z and places the result in worktable EZ (block **1620**).

If the join condition is a not equal condition (block **1605**), the system generates a Cartesian product of partitions D and Y and places the result in worktable DY (block **1625**). The system generates a Cartesian product of partitions D and Z and places the result in worktable DZ (block **1630**). The system generates a Cartesian product of partitions F and X and places the result in worktable FX (block **1635**). The system generates a Cartesian product of partitions F and Y and places the result in worktable FY (block **1640**). The system generates a Cartesian product of partitions E and X and places the result in worktable EX (block **1645**). The system generates a Cartesian product of partitions E and Z and places the result in worktable EZ (block **1650**).

Other example systems perform the Cartesian products differently. One example system replaces the series of Cartesian products within block **1655**. The example system, shown in FIG. 17 replaces blocks **1625**-**1640** (FIG. 16) with one Cartesian product. The system merges partitions D and F and places the result in DF (block **1705**). The system merges partitions X, Y, and Z, and places the result in XYZ (block **1710**). The system generates the Cartesian product of DF and XYZ and places the result in DFXYZ (block **1715**). In this example system, the Cartesian products of partitions D and Y, D and Z, F and X, and F and Y are represented by DFXYZ.

Returning to FIG. 5, the system performs the SQL query on a partition of T**1**.A and a partition of T**2**.B to produce a partial query result (block **530**). An example system for performing the SQL query is shown in FIG. 18. The system performs the SQL query on partitions E and Y and places the result in a worktable EY (block **1805**). An example query for performing the SQL query is:

SELECT E.*, Y.* FROM E, Y WHERE E.A condition Y.B;

where condition is the condition in the SQL query.

Returning to FIG. 5, the system merges Cartesian products and query results (block **535**).

FIG. 19 shows a system for merging the Cartesian products and query results. The system determines if the join condition is a not equal condition (block **1905**). If the join condition is not a not equal condition, the system merges the worktables DY, DZ, EZ, and EY (block **1910**), otherwise the system merges the worktables DY, DZ, FX, FY, EX, EZ, and EY (block **1915**).

In one example system, where the Cartesian product DFXYZ was generated in place of DY, DZ, FX, and FY (block **1655** in FIGS. 16, **17**), the example system merges the worktables DFXYZ, EX, EZ, and EY.

The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.

1. A method of performing a database query to join a column A and a column B on an inequality condition, the method including:

determining a minimum and a maximum value for A, using a value-count index for A, the value-count index for A including which values appear in A and how many times the values appear in A;

determining a minimum and a maximum value for B, using a value-count index for B, the value-count index for B including which values appear in B and how many times the values appear in B;

defining three or more sets of values in A, relative to the minimum and maximum values for B;

defining three or more sets of values in B, relative to the minimum and maximum values for A;

generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;

performing the database query on a set of values in A and a set of values in B to generate a partial query result;

merging one or more Cartesian products and the partial query result; and

storing the merged one or more Cartesian products and the partial query result.

determining a minimum and a maximum value for A, using a value-count index for A, the value-count index for A including which values appear in A and how many times the values appear in A;

determining a minimum and a maximum value for B, using a value-count index for B, the value-count index for B including which values appear in B and how many times the values appear in B;

defining three or more sets of values in A, relative to the minimum and maximum values for B;

defining three or more sets of values in B, relative to the minimum and maximum values for A;

generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;

performing the database query on a set of values in A and a set of values in B to generate a partial query result;

merging one or more Cartesian products and the partial query result; and

storing the merged one or more Cartesian products and the partial query result.

2. The method of claim 1, where determining a minimum and a maximum value for A, using the value-count index for A includes:

scanning the value-count index for A to determine the minimum value for A and the maximum value for A.

scanning the value-count index for A to determine the minimum value for A and the maximum value for A.

3. The method of claim 1, where determining a minimum and a maximum value for B, using the value-count index for B includes:

scanning the value-count index for B to determine the minimum value for B and the maximum value for B.

scanning the value-count index for B to determine the minimum value for B and the maximum value for B.

4. The method of claim 1, where column A is in a table T**1** including zero or more rows and one or more columns, and where defining three sets of values in A, relative to the minimum and maximum values for B includes:

for each row in T**1**:

if A is less than the minimum value for B, projecting one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, projecting one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, projecting one or more columns from the row into a partition F.

for each row in T**1**:

if A is less than the minimum value for B, projecting one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, projecting one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, projecting one or more columns from the row into a partition F.

if A is less than the minimum value for B, projecting one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, projecting one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, projecting one or more columns from the row into a partition F.

5. The method of claim 4, where column B is in a table T**2** including zero or more rows and one or more columns, and where defining three sets of values in B, relative to the minimum and maximum values for A includes:

for each row in T**2**:

if B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, projecting one or more columns from the row into a partition Z.

for each row in T**2**:

if B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, projecting one or more columns from the row into a partition Z.

if B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, projecting one or more columns from the row into a partition Z.

6. The method of claim 5, where the inequality condition is a “less than” or a “less than” or “equal” condition, and where generating one or more Cartesian products includes:

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z; and

generating a Cartesian product of partition E and partition Z.

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z; and

generating a Cartesian product of partition E and partition Z.

7. The method of claim 5, where the inequality condition is a “less than” or a “less than or equal” condition, and where performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y.

performing the database query on partition E and partition Y.

8. The method of claim 7, where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

merging:

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

9. The method of claim 5, where the inequality condition is a “not equal” condition, and where generating one or more Cartesian products includes:

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z;

generating a Cartesian product of partition E and partition X;

generating a Cartesian product of partition E and partition Z;

generating a Cartesian product of partition F and partition X; and

generating a Cartesian product of partition F and partition Y.

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z;

generating a Cartesian product of partition E and partition X;

generating a Cartesian product of partition E and partition Z;

generating a Cartesian product of partition F and partition X; and

generating a Cartesian product of partition F and partition Y.

10. The method of claim 9, where:

performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

performing the database query on partition E and partition Y;

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

11. The method of claim 5, where the inequality condition is a “not equal” condition, and where generating one or more Cartesian products includes:

merging partition D and partition F to form a partition DF;

merging partition X, partition Y, and partition Z to for a partition XYZ;

generating a Cartesian product of partition DF and partition XYZ.

merging partition D and partition F to form a partition DF;

merging partition X, partition Y, and partition Z to for a partition XYZ;

generating a Cartesian product of partition DF and partition XYZ.

12. The method of claim 11, where:

performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

performing the database query on partition E and partition Y;

merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

13. The method of claim 5, where the inequality condition is a “not equal” condition, and where performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y.

performing the database query on partition E and partition Y.

14. The method of claim 1, where the inequality condition is a “less than or equal” condition or a “greater than or equal” condition, where column A is in a table T**1** including zero or more rows and one or more columns, and where defining three sets of values in A, relative to the minimum and maximum values for B includes:

for each row in T**1**:

if T**1**.A is less than or equal to the minimum value for B, projecting one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, projecting one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, projecting one or more columns from the row into a partition F.

for each row in T**1**:

if T**1**.A is less than or equal to the minimum value for B, projecting one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, projecting one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, projecting one or more columns from the row into a partition F.

if T**1**.A is less than or equal to the minimum value for B, projecting one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, projecting one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, projecting one or more columns from the row into a partition F.

15. The method of claim 14, where column B is in a table T**2** including zero or more rows and one or more columns, and where defining three sets of values in B, relative to the minimum and maximum values for A includes:

for each row in T**2**:

if T**2**.B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, projecting one or more columns from the row into a partition Z.

for each row in T**2**:

if T**2**.B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, projecting one or more columns from the row into a partition Z.

if T**2**.B is less than the minimum value for A, projecting one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, projecting one or more columns from the row into a partition Z.

16. The method of claim 1, where the inequality condition is a “greater than” condition, the method including:

converting the query to a query including a “less than” inequality condition.

converting the query to a query including a “less than” inequality condition.

17. The method of claim 1, where the inequality condition is a “greater than or equal to” condition, the method including:

converting the query to a query including a “less than or equal to” inequality condition.

converting the query to a query including a “less than or equal to” inequality condition.

18. A computer program, stored on a tangible storage medium, for use in performing a database query to join a column A and a column B on an inequality condition, the computer program including executable instructions that cause a computer to:

determine a minimum and a maximum value for A, using a value-count index for A, the value-count index for A including which values appear in A and how many times the values appear in A;

determine a minimum and a maximum value for B, using a value-count index for B, the value-count index for B including which values appear in B and how many times the values appear in B;

define three or more sets of values in A, relative to the minimum and maximum values for B;

define three or more sets of values in B, relative to the minimum and maximum values for A;

generate one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;

perform the database query on a set of values in A and a set of values in B to generate a partial query result;

merge one or more Cartesian products and the result; and

storing the merged one or more Cartesian products and the result.

determine a minimum and a maximum value for A, using a value-count index for A, the value-count index for A including which values appear in A and how many times the values appear in A;

determine a minimum and a maximum value for B, using a value-count index for B, the value-count index for B including which values appear in B and how many times the values appear in B;

define three or more sets of values in A, relative to the minimum and maximum values for B;

define three or more sets of values in B, relative to the minimum and maximum values for A;

generate one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;

perform the database query on a set of values in A and a set of values in B to generate a partial query result;

merge one or more Cartesian products and the result; and

storing the merged one or more Cartesian products and the result.

19. The computer program of claim 18, where the executable instructions that cause the computer to determine a minimum and a maximum value for A, using the value-count index for A further cause the computer to:

scan the value-count index for A to determine the minimum value for A and the maximum value for A.

scan the value-count index for A to determine the minimum value for A and the maximum value for A.

20. The computer program of claim 18, where the executable instructions that cause the computer to determine a minimum and a maximum value for B, using the value-count index for B further cause the computer to:

scan the value-count index for B to determine the minimum value for B and the maximum value for B.

scan the value-count index for B to determine the minimum value for B and the maximum value for B.

21. The computer program of claim 18, where column A is in a table T**1** including zero or more rows and one or more columns, and where the executable instructions that cause the computer to define three sets of values in A, relative to the minimum and maximum values for B further cause the computer to:

for each row in T**1**:

if A is less than the minimum value for B, project one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, project one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, project one or more columns from the row into a partition F.

for each row in T**1**:

if A is less than the minimum value for B, project one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, project one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, project one or more columns from the row into a partition F.

if A is less than the minimum value for B, project one or more columns from the row into a partition D;

if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, project one or more columns from the row into a partition E; and

if A is greater than the maximum value for B, project one or more columns from the row into a partition F.

22. The computer program of claim 21, where column B is in a table T**2** including zero or more rows and one or more columns, and where the executable instructions that cause the computer to define three sets of values in B, relative to the minimum and maximum values for A further cause the computer to:

for each row in T**2**:

if B is less than the minimum value for A, project one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, project one or more columns from the row into a partition Z.

for each row in T**2**:

if B is less than the minimum value for A, project one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, project one or more columns from the row into a partition Z.

if B is less than the minimum value for A, project one or more columns from the row into a partition X;

if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if B is greater than the maximum value for A, project one or more columns from the row into a partition Z.

23. The computer program of claim 22, where the inequality condition is a “less than” or a “less than or equal” condition, and where the executable instructions that cause the computer to generate one or more Cartesian products further cause the computer to:

generate a Cartesian product of partition D and partition Y;

generate a Cartesian product of partition D and partition Z; and

generate a Cartesian product of partition E and partition Z.

generate a Cartesian product of partition D and partition Y;

generate a Cartesian product of partition D and partition Z; and

generate a Cartesian product of partition E and partition Z.

24. The computer program of claim 22, where the inequality condition is a “less than” or a “less than or equal” condition, and where the executable instructions that cause the computer to perform the database query on a set of values in A and a set of values in B to generate a partial query result further cause the computer to:

perform the database query on partition E and partition Y.

perform the database query on partition E and partition Y.

25. The computer program of claim 24, where the executable instructions that cause the computer to merge one or more Cartesian products and the partial query result further cause the computer to:

merge:

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

merge:

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

26. The computer program of claim 24, where the inequality condition is a “not equal” condition, and where the executable instructions that cause the computer to generate one or more Cartesian products further cause the computer to:

generate a Cartesian product of partition D and partition Y;

generate a Cartesian product of partition D and partition Z;

generate a Cartesian product of partition E and partition X;

generate a Cartesian product of partition E and partition Z;

generate a Cartesian product of partition F and partition X; and

generate a Cartesian product of partition F and partition Y.

generate a Cartesian product of partition D and partition Y;

generate a Cartesian product of partition D and partition Z;

generate a Cartesian product of partition E and partition X;

generate a Cartesian product of partition E and partition Z;

generate a Cartesian product of partition F and partition X; and

generate a Cartesian product of partition F and partition Y.

27. The computer program of claim 26, where the executable instructions that cause the computer to:

perform the database query on a set of values in A and a set of values in B to generate a partial query result further cause the computer to:

perform the database query on partition E and partition Y;

and where the executable instructions that cause the computer to merge one or more Cartesian products and the partial query result further cause the computer to:

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

perform the database query on a set of values in A and a set of values in B to generate a partial query result further cause the computer to:

perform the database query on partition E and partition Y;

and where the executable instructions that cause the computer to merge one or more Cartesian products and the partial query result further cause the computer to:

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

perform the database query on partition E and partition Y;

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

28. The computer program of claim 22, where the inequality condition is a “not equal” condition, and where the executable instructions that cause the computer to generate one or more Cartesian products further cause the computer to:

merge partition D and partition F to form a partition DF;

merge partition X, partition Y, and partition Z to for a partition XYZ; and

generate a Cartesian product of partition DF and partition XYZ.

merge partition D and partition F to form a partition DF;

merge partition X, partition Y, and partition Z to for a partition XYZ; and

generate a Cartesian product of partition DF and partition XYZ.

29. The computer program of claim 28, where the executable instructions that cause the computer to:

perform the database query on a set of values in A and a set of values in B to generate a partial query result further cause the computer to:

perform the database query on partition E and partition Y;

and where the executable instructions that cause the computer to merge one or more Cartesian products and the partial query result further cause the computer to:

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

perform the database query on partition E and partition Y;

and where the executable instructions that cause the computer to merge one or more Cartesian products and the partial query result further cause the computer to:

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

perform the database query on partition E and partition Y;

merge:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

30. The computer program of claim 22, where the inequality condition is a “not equal” condition, and where the executable instructions that cause the computer to perform the database query on a set of values in A and a set of values in B to generate a partial query result further cause the computer to:

perform the database query on partition E and partition Y.

perform the database query on partition E and partition Y.

31. The computer program of claim 18, where the inequality condition is a “less than or equal” condition or a “greater than or equal” condition, where column A is in a table T**1** including zero or more rows and one or more columns, and where the executable instructions that cause the computer to define three sets of values in A, relative to the minimum and maximum values for B further cause the computer to:

for each row in T**1**:

if T**1**.A is less than or equal to the minimum value for B, project one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, project one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, project one or more columns from the row into a partition F.

for each row in T**1**:

if T**1**.A is less than or equal to the minimum value for B, project one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, project one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, project one or more columns from the row into a partition F.

if T**1**.A is less than or equal to the minimum value for B, project one or more columns from the row into a partition D;

if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, project one or more columns from the row into a partition E; and

if T**1**.A is greater than or the maximum value for B, project one or more columns from the row into a partition F.

32. The computer program of claim 31, where column B is in a table T**2** including zero or more rows and one or more columns, and where the executable instructions that cause the computer to define three sets of values in B, relative to the minimum and maximum values for A further cause the computer to:

for each row in T**2**:

if T**2**.B is less than the minimum value for A, project one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, project one or more columns from the row into a partition Z.

for each row in T**2**:

if T**2**.B is less than the minimum value for A, project one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, project one or more columns from the row into a partition Z.

if T**2**.B is less than the minimum value for A, project one or more columns from the row into a partition X;

if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, project one or more columns from the row into a partition Y; and

if T**2**.B is greater than or equal to the maximum value for A, project one or more columns from the row into a partition Z.

33. The computer program of claim 18, where the inequality condition is a “greater than” condition, the executable instructions that cause the computer further causing the computer to:

convert the query to a query including a “less than” inequality condition.

convert the query to a query including a “less than” inequality condition.

34. The computer program of claim 18, where the inequality condition is a “greater than or equal to” condition, the executable instructions that cause the computer further causing the computer to:

convert the query to a query including a “less than or equal to” inequality condition.

convert the query to a query including a “less than or equal to” inequality condition.

35. A database system including:

a massively parallel processing system including:

one or more nodes;

a plurality of CPUs, each of the one or more nodes providing access to one or more CPUs;

a plurality of data storage facilities each of the one or more CPUs providing access to one or more data storage facilities;

a process for execution on the massively parallel processing system for performing a database query to join a column A and a column B on an inequality condition, a database including value-count indexes for columns A and B, the value-count index for A including which values appear in A and how many times the values appear in A, the value-count index for B including which values appear in B and how many times the values appear in B, the process including:

determining a minimum and a maximum value for A, using the value-count index for A;

determining a minimum and a maximum value for B, using the value-count index for B;

defining three or more sets of values in A, relative to the minimum and maximum values for B;

defining three or more sets of values in B, relative to the minimum and maximum values for A;

generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;

performing the database query on a set of values in A and a set of values in B to generate a partial query result;

merging one or more Cartesian products and the partial query result; and

storing the merged one or more Cartesian products and the partial query result.

a massively parallel processing system including:

one or more nodes;

a plurality of CPUs, each of the one or more nodes providing access to one or more CPUs;

a plurality of data storage facilities each of the one or more CPUs providing access to one or more data storage facilities;

a process for execution on the massively parallel processing system for performing a database query to join a column A and a column B on an inequality condition, a database including value-count indexes for columns A and B, the value-count index for A including which values appear in A and how many times the values appear in A, the value-count index for B including which values appear in B and how many times the values appear in B, the process including:
generating one or more Cartesian products, where each Cartesian product is between a set of values in A and a set of values in B;
performing the database query on a set of values in A and a set of values in B to generate a partial query result;

determining a minimum and a maximum value for A, using the value-count index for A;

determining a minimum and a maximum value for B, using the value-count index for B;

defining three or more sets of values in A, relative to the minimum and maximum values for B;

defining three or more sets of values in B, relative to the minimum and maximum values for A;

merging one or more Cartesian products and the partial query result; and

storing the merged one or more Cartesian products and the partial query result.

determining a minimum and a maximum value for A, using the value-count index for A;

determining a minimum and a maximum value for B, using the value-count index for B;

defining three or more sets of values in A, relative to the minimum and maximum values for B;

defining three or more sets of values in B, relative to the minimum and maximum values for A;

merging one or more Cartesian products and the partial query result; and

storing the merged one or more Cartesian products and the partial query result.

36. The database system of claim 35, where determining a minimum and a maximum value for A, using the value-count index for A includes:

scanning the value-count index for A to determine the minimum value for A and the maximum value for A.

37. The database system of claim 35, where determining a minimum and a maximum value for B, using the value-count index for B includes:

scanning the value-count index for B to determine the minimum value for B and the maximum value for B.

38. The database system of claim 35, where column A is in a table T**1** including zero or more rows and one or more columns, and where defining three sets of values in A, relative to the minimum and maximum values for B includes:

for each row in T**1**:
if A is less than the minimum value for B, projecting one or more columns from the row into a partition D;
if A is less than or equal to the maximum value for B and T**1**.A is greater than or equal to the minimum value for B, projecting one or more columns from the row into a partition E; and
if A is greater than the maximum value for B, projecting one or more columns from the row into a partition F.

39. The database system of claim 38, where column B is in a table T**2** including zero or more rows and one or more columns, and where defining three sets of values in B, relative to the minimum and maximum values for A includes:

for each row in T**2**:
if B is less than the minimum value for A, projecting one or more columns from the row into a partition X;
if B is less than or equal to the maximum value for A and T**1**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and
if B is greater than the maximum value for A, projecting one or more columns from the row into a partition Z.

40. The database system of claim 39, where the inequality condition is a “less than” or a “less than or equal” condition, and where generating one or more Cartesian products includes:

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z; and

generating a Cartesian product of partition E and partition Z.

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z; and

generating a Cartesian product of partition E and partition Z.

41. The database system of claim 39, where the inequality condition is a “less than” or a “less than or equal” condition, and where performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y.

performing the database query on partition E and partition Y.

42. The database system of claim 41, where merging one or more Cartesian products and the partial query result includes:

merging:

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

a Cartesians product of partition D and partition Y;

a Cartesian product of partition D and partition Z; and

a Cartesian product of partition E and partition Z.

43. The database system of claim 39, where the inequality condition is a “not equal” condition, and where generating one or more Cartesian products includes:

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z;

generating a Cartesian product of partition E and partition X;

generating a Cartesian product of partition E and partition Z;

generating a Cartesian product of partition F and partition X; and

generating a Cartesian product of partition F and partition Y.

generating a Cartesian product of partition D and partition Y;

generating a Cartesian product of partition D and partition Z;

generating a Cartesian product of partition E and partition X;

generating a Cartesian product of partition E and partition Z;

generating a Cartesian product of partition F and partition X; and

generating a Cartesian product of partition F and partition Y.

44. The database system of claim 43, where:
performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:
merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

performing the database query on partition E and partition Y;

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

performing the database query on partition E and partition Y;

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition D and partition Y;

the Cartesian product of partition D and partition Z;

the Cartesian product of partition E and partition X;

the Cartesian product of partition E and partition Z;

the Cartesian product of partition F and partition X; and

the Cartesian product of partition F and partition Y.

45. The database system of claim 39, where the inequality condition is a “not equal” condition, and where generating one or more Cartesian products includes:

merging partition D and partition F to form a partition DF;

merging partition X, partition Y, and partition Z to for a partition XYZ; and

generating a Cartesian product of partition DF and partition XYZ.

merging partition D and partition F to form a partition DF;

merging partition X, partition Y, and partition Z to for a partition XYZ; and

generating a Cartesian product of partition DF and partition XYZ.

46. The database system of claim 45, where:
performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y;

and where merging one or more Cartesian products and the partial query result includes:
merging:

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

performing the database query on partition E and partition Y;

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

performing the database query on partition E and partition Y;

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

the partial query result of the database query on partition E and partition Y;

the Cartesian product of partition DF and partition XYZ;

the Cartesian product of partition E and partition X; and

the Cartesian product of partition E and partition Z.

47. The database system of claim 39, where the inequality condition is a “not equal” condition, and where performing the database query on a set of values in A and a set of values in B to generate a partial query result includes:

performing the database query on partition E and partition Y.

performing the database query on partition E and partition Y.

48. The database system of claim 35, where the inequality condition is a “less than or equal” condition or a “greater than or equal” condition, where column A is in a table T**1** including zero or more rows and one or more columns, and where defining three sets of values in A, relative to the minimum and maximum values for B includes:

for each row in T**1**:
if T**1**.A is less than or equal to the minimum value for B, projecting one or more columns from the row into a partition D;
if T**1**.A is less than or equal to the maximum value for B and T**1**.A is greater than the minimum value for B, projecting one or more columns from the row into a partition E; and
if T**1**.A is greater than or the maximum value for B, projecting one or more columns from the row into a partition F.

49. The database system of claim 48, where column B is in a table T**2** including zero or more rows and one or more columns, and where defining three sets of values in B, relative to the minimum and maximum values for A includes:

for each row in T**2**:
if T**2**.B is less than the minimum value for A, projecting one or more columns from the row into a partition X;
if T**2**.B is less than the maximum value for A and T**2**.B is greater than or equal to the minimum value for A, projecting one or more columns from the row into a partition Y; and
if T**2**.B is greater than or equal to the maximum value for A, projecting one or more columns from the row into a partition Z.

50. The database system of claim 35, where the inequality condition is a “greater than” condition, the process including:

converting the query to a query including a “less than” inequality condition.

converting the query to a query including a “less than” inequality condition.

51. The database system of claim 35, where the inequality condition is a “greater than or equal to” condition, the process including:

converting the query to a query including a “less than or equal to” inequality condition.

converting the query to a query including a “less than or equal to” inequality condition.