Cost based optimization of decision support queries using transient views6275818Abstract The present invention discloses a method, apparatus, and article of manufacture for optimizing one or more queries. Initially, redundancies in execution steps for the one or more queries are identified. Then, a new set of equivalent execution steps is created by eliminating redundancies in the execution steps. The new set of equivalent execution steps is used to execute the one or more queries when the use results in efficient query processing. Claims What is claimed is: Description BACKGROUND OF THE INVENTION
TABLE 1
Plan Properties
Property Notation Example
Tables in the plan T.sub.i Relation T1, T2
Columns selected Cols.sub.i C1, C2, C3
Join predicates J P.sub.i T1.C1 RelOp T2.C2
Set of simple predicates S P.sub.i T1.C1 RelOp Constant
Aggregation Functions Af.sub.i (Exp) SUM, MIN, MAX, AVG
Columns in the group by list GC.sub.i GROUP BY C1, C2, C3
Data source plan executes S.sub.i DB2, WEB SERVER,
ORACLE
Cost of executing plan Cost.sub.i Time in ms
Number of result rows Card.sub.i Number of Tuples
These properties correspond to the information necessary to reconstruct a single block query for which the plan was generated. In the preferred embodiment of the invention, transient-views are created that correspond to single block queries. The single block query consists of a SELECT list that contains columns and aggregation functions, a set of tables in the from clause, and a set of simple predicates (col relop value) and JOIN predicates. The GROUP BY list contains a set of columns that are a super-set of the columns on the SELECT list. Each entity required to construct the single block query is listed in the property list. Additionally the cost and the cardinality information are also maintained Operators: The following operators are building blocks for the query plan: SCAN, JOIN, GROUP BY, RQUERY. These operators were chosen because they sufficiently describe the plan tree of a single block query with the properties in Table 1 above. The SCAN, JOIN, and GROUP BY operators do not need any introduction. RQUERY is a novel operator that is unique to a setting consisting of remote data sources. It encapsulates the job (sub-plan) to be performed at a remote source. Thus, the unit of work `beneath` this operator is performed at the remote source, and the data that is returned as a result of this execution is shipped to the local site. Each operator receives a plan or a set of plans and their associated properties as input and produces a plan with a modified set of properties as output. Thus, the properties of a plan are recursively built using the plan operators. Table 2 presents the operators in column1. The input properties associated with the operators are presented in column 2 of Table 2.
TABLE 2
Operators and Properties
Operator Input Parameter
SCAN Type (scan vs iscan)
Name of Table
Simple Predicates
Columns selected
JOIN Method (merge, nested . . . )
Outer Plan
Inner Plan
Join Predicates
GROUP BY Columns in select
Aggregation Functions
Group By list
RQUERY Input plan
Data source
To illustrate the above concepts, an example of a query and its corresponding plan tree is presented below. Example: Consider the following query in the context of the investor's application. Display the investor names and their current investment value in technology stocks and oil stocks for those investors for whom the average trading volumes of the technology and oil stocks in their portfolio was higher than the market trading volume of oil and technology stocks. Consider only those stocks in the portfolio that were bought prior to `Oct. 1, 1997`. To better understand the syntax for this query, two views are defined. Note, that it is not necessary to define views to express the query. Views are defined in the application to illustrate the syntax of the query. The following view retrieves the name, the average volume, and the net value of the investments in technology stocks of companies located in the silicon valley.
CREATE VIEW Tech (invest_name, invest_id, vol, cnt, value) AS
SELECT Rinvest.name, SUM(Wstock.volume), COUNT
(Wstock.volume),
SUM (Rinvest.qty*Wstock.price)
FROM Rinvest, Wstock
WHERE Rinvest.ticker=Wstock.ticker
AND Wstock.cat=`Tech`
AND Wstock.date =`11/03/97`
AND Rinvest.buy <`10/01/97`
GROUP BY Rinvest.name
The following view retrieves the name, the average volume, and the net value of the investments in technology stocks of companies located in the silicon valley.
CREATE VIEW Oil (invest_name, invest_id, cnt, value) AS
SELECT Rinvest.name, Rinvest.id, AVG(Wstock.volume),
COUNT(Wstock.volume),
SUM(Rinvest.qty*Wstock.price)
FROM Rinvest, Wstock
WHERE Rinvest.ticker=Wstock.ticker
AND Wstock.cat=`Oil`
AND Wstock.date=`11/03/97`
AND Rinvest.by <`10/01/97`
GROUP BY Rinvest.name
SELECT Oil.invest-name, Oil.value, Tech.value
FROM Oil. Tech
WHERE Oil.invest_id = Tech.invest_id
AND (Oil.vol+Tech.vol)/(Oil.cnt+Tech.cnt)>(SELECT
avg(Wstock.volume)
FROM Wstock
WHERE (Wstock.category=`Tech`
OR Wstock.category=`Oil`
AND Wstock.date = `11/03/97`
Hardware Environment FIG. 1 illustrates an exemplary computer hardware environment that could be used in accordance with the present invention. In the exemplary environment, a Client computer system 100 transmits user queries to a DBMS 102. The Client computer 100 may be comprised, inter alia, of one or more processors, one or more input devices (e.g., a mouse or keyboard), one or more data storage devices (e.g., a fixed or hard disk drive, a floppy disk drive, a CDROM drive, or a tape drive), or other devices. The user queries represent commands for performing various search and retrieval functions, termed queries, against the DBMS 102. The DBMS 102 resides on a computer system. In one embodiment of the present invention, these queries conform to the Structured Query Language (SQL) standard and invoke functions performed by the DBMS 102. The SQL interface has evolved into a standard language for DBMS 102 and has been adopted as such by both the American National Standards Institute (ANSI) and the International Standards Organization (ISO). The SQL interface allows users to formulate relational operations on the tables either interactively, in batch files, or embedded in host languages, such as C and COBOL. SQL allows the user to manipulate the data. Those skilled in the art will recognize, however, that the present invention has application to any DBMS, whether or not the DBMS uses SQL. In the preferred embodiment of the present invention, the DBMS 102 is comprised of layers 104, 106, 108, and 110. The Client Communication Services layer 104 receives the user queries and forwards them to the next layer 106. A Cost Based Optimizer 112 works in conjunction with a Catalog Services module 114, a Transaction Manager 116, and a Runtime Service module 118 to process the user queries. The Runtime Service module 118 executes the user queries in conjunction with the next layer 108, containing a Buffer Manager 120, a Lock Manager 122, a Remote Services module 124, and other modules 126. The Buffer Manager 120 and other modules work in conjunction with a Physical Disk Layer 128 to connect to a database 132 and retrieve data from the database 132. The Remote Services module 124 and other modules work in conjunction with the Remote Comm module 130 to connect to remote systems 134 and 136, each of which is connected to separate databases. Generally, the DBMS, the SQL statements, and the instructions derived therefrom, are all tangibly embodied in a computer-readable medium, e.g. one or more of the data storage devices. Moreover, the DBMS, the SQL statements, and the instructions derived therefrom, are all comprised of instructions which, when read and executed by a computer system, causes the computer system to perform the steps necessary to implement and/or use the present invention. Under control of an operating system, the DBMS software, the SQL statements, and the instructions derived therefrom, may be loaded from the data storage devices into a memory of a computer system for use during actual operations. Thus, the present invention may be implemented as a method, apparatus, or article of manufacture using standard programming and/or engineering techniques to produce software, firmware, hardware, or any combination thereof. The term "article of manufacture" (or alternatively, "computer program product") as used herein is intended to encompass a computer program accessible from any computer-readable device, carrier, or media. Of course, those skilled in the art will recognize many modifications may be made to this configuration without departing from the scope of the present invention. Those skilled in the art will recognize that the exemplary environment illustrated in FIG. 1 is not intended to limit the present invention. Indeed, those skilled in the art will recognize that other alternative hardware environments may be used without departing from the scope of the present invention. Architecture In this application, the Cost Based Optimizer 112 is implemented and realized in the context of the HDBS architecture 200 shown in FIG. 2. Those skilled in the art will recognize that other architectures may be used without departing from scope of the present invention. The HDBS architecture 200 is somewhat similar to the DataJoiner multi-database system, Shivakumar Venkataraman and Tian Zhang, DataJoiner Optimizer: Optimizing Query for Heterogeneous Database Systems, VLDB 98, New York, [hereinafter "[ea97]"], which is incorporated by reference herein. The HDBS architecture 200 provides a single database image to tables (or table views obtained via relational wrappers) in multiple data sources. The database clients, 202, 204, and 206 access remote tables as though they were local, through user defined aliases. The presence of remote data sources 208, 210, and 212 is completely transparent to the user. The user submits queries as though the queries were directed to local tables and receives results as though they would have been generated on local tables. Queries submitted to the HDBS may access both the local and remote tables. The HDBS query processor 214 rewrites these queries, applies cost-based optimization to determine which parts of the queries should be executed locally, and which should be executed on the remote sources 208, 210, and 212. The parts of the query that should be executed remotely are translated to the lingua-franca (in the case of SQL databases, to the appropriate SQL dialects) of the remote sources 208, 210, and 212 and sent to the remote sources 208, 210, and 212 for execution. The results received are translated, converted to local types, and combined with the results of queries on local tables and returned to the clients 202, 204, and 206. Ouery Optimizer The Cost Based Optimizer 112 is based on the well-known STARBURST relational query optimizer, P. Gassner, G. M. Lohman, and Y Schiefer, B. Wang, Query Optimization in the IBM DB2 Family, Data Engineering Bulletin, 16(4), 1993, [hereinafter "[GLS93]"], which is incorporated by reference herein, extended to a HDBS architecture 200 setting. FIG. 3 shows the stages that a query goes through in the optimizer before it is executed. Following is a brief description of how a query plan is created: Parser: A query 300 from a user is first parsed, semantically analyzed, and translated into a chosen internal representation, as represented by block 302 Query Rewrite: The output of the parser is transformed by a set of rewrite rules, as represented by block 304, H. Pirahesh, J. M Hellerstein, and W. Hassan, Extensible/Rule Based Query Rewrite Optimization in Starburst, In Proceedings of the ACM SIGMOD Conference, pages 39-48, 1992, [hereinafter "[PHH92]"], which is incorporated by reference herein. These rewrite rules are usually heuristics aiding in transforming the query representation into a better form in order for the query optimizer 306 to search a larger space for an optimal plan. Query Optimizer: The query optimizer uses the rewritten query as input to generate query plans based on the capabilities of the remote data source, as represented by block 306. Code Generation: Code is generated for those portions of the query that needs to be executed locally as well as remotely, as represented by block 312. The output 314 is also shown. FIG. 3 shows how the transient view module 308 fits in the above query processing architecture. The transient view module 308 takes as input the optimizer plan and produces a plan that consists of transient views. The Cost Based Optimizer 310 (see 112 in FIG. 1) performs a comparison between the performance of the plan that contains transient views and the performance of the plan produced by the query optimizer 306 to determine whether the transient views improve the performance of the plan. Equivalence of Sub-plans FIG. 4 shows a query plan tree that is generated by the query optimizer 306. The nodes in the plan tree generated by the query optimizer 306 are labeled so that equivalent nodes can be identified. Transient materialized views are created from the query optimizer 306 plan tree. The transient views are used to avoid redundant computations by combining redundant sub-plans. The preferred embodiment of the invention identifies redundant sub-plans that represent one query block. Specifically, equivalent parts of the query plan are identified and combined so that redundancy is avoided. The notion of equivalence is quite broad in that the combined parts might have a result that is a superset of the result of each subpart. For instance, two plan trees may be identified as equivalent if a set of properties can be defined which represent a single block query that can produce the union of the result of the two plan trees. For example, two scan operators that operate on identical tables but apply different predicates would be considered equivalent. A new scan operator can be defined that can apply the combination of the two predicates, and obtain the results that would have been generated by the two scan operators. The predicates that the scan operators originally had as filters can be applied on the result generated from the new scan operator. Note that the problem of identifying equivalent sub-plans in a plan that was generated by the query optimizer 306 is essentially the problem of identifying equivalent sub-trees in a tree. Equivalence is defined based on induction. Equivalence of nodes is the base case. The following is the definition of equivalence. Let n.sub.1 and n.sub.2 be two nodes of a plan tree T. A relation.about.on nodes of T is defined as follows. For each case, if the requirements below are met, then n.sub.1.about.n.sub.2. 1. tables--n.sub.1 and n.sub.2 should be identical; 2. SCAN operators--their properties should agree as defined in Table 3; 3. JOIN operators--their properties should agree as defined in Table 4; 4. GROUP BY operators--their properties should agree as defined in Table 5; and 5. ROUERY operators--their properties should agree as defined in Table 6. The relation.ident.is the symmetric, reflexive, transitive closure of.about.. Thus, .ident. is an equivalence relation. Note that by the above definition and the requirements imposed on the properties, the equivalence of two nodes n.sub.1 and n.sub.2 implies equivalence of the two sub-plans that respectively have n.sub.1 and n.sub.2 as their root. The rationale behind the choice of the equivalence conditions is now presented. SCAN: A scan operator operates on one table and applies a set of predicates to the table and produces a set of columns as the result. Two scan operators are equivalent if they differ only in their column selected and the simple predicates that are applied. The scan operator that produces the union of the result of the two scans consists of the union of the columns in the two scan operators and has predicates that is the OR of the predicates in the two scan operators. The filter query for each scan operator projects out the columns and applies the predicates required by the SCAN.
TABLE 3
Scan Properties
Property Condition
Scan type Identical (eg: table or index scan)
Table scanned Identical
Set of simple predicates does not matter
Columns selected does not matter
JOIN: A join operator takes two plans as input and joins the two plans based on one or more predicates. There are several join methods to implement this operator. Two join operators are defined to be equivalent if the join method employed by them is identical. The inner plans for the join operators have to belong to the same equivalence class. The outer plans also have to belong to the same equivalence class. The join predicates have to be identical. Pulling up all the simple predicates from the two join operators produces two trees that are identical, except, for the columns that are fetched and the pulled up predicates. This is because, every node, below the join operator is equivalent The combined join operator for these two join operators can be viewed as one that has an identical tree but has the OR of the simple predicates in these two plans applied. The filter queries consists of applying the simple predicate filter and column projection to the result of the combined join operator.
TABLE 4
Join Properties
Property Condition
Join method Identical
Outer plan Equivalent
Inner plan Equivalent
Join predicates Identical
GROUP BY: The GROUP BY operator takes an input plan and applies aggregation functions to the columns of the input plan by grouping the columns on the GROUP BY list. Two GROUP BY operators are considered to be equivalent if the plans that are input to the GROUP BY are in the same equivalence class. Specifically, the columns in the GROUP BY list of one operator must be a complete subset of the columns in the GROUP BY list of the other group by list. This restriction helps to confirm whether combining the two GROUP BY operations improves performance. For the disjunctive predicates that are not identical in the plan's input to the GROUP BY operator, columns referenced in the simple predicate are placed in the SELECT list and the GROUP BY list property of the combined plan. This ensures that the aggregation function compute the right result.
TABLE 5
Group By Properties
Property Condition
Input plan Equivalent
Columns in the SELECT list does not matter
Aggregation Functions does not matter
Group by list containment and add
columns from the simple
predicate
RQUERY: The remote query operator represents the boundary with the remote database. It represents the point at which the results are fetched from the remote database. Two remote query operators are equivalent if the plans that the remote query operation are a part of are in the same equivalence class and the two queries are directed towards the same data source.
TABLE 6
Rquery Properties
Property Condition
Input plan Equivalent
Data source where plan executes Identical
Multi-Block Queries Recall from the discussions in the previous section that each of the plan operators yields a plan with a set of properties that can be described as in Table 1. However, Table 1 is not sufficient to describe the properties that result from the application of certain operators such as UNION. The property of the plan after applying the UNION operator consists of the union of the properties of the individual sub-plans and hence cannot be described using the table. These queries are called multi-block queries. Multi-block queries can be handled in the framework by extending the property by adding a property set that represent the union of the properties of the plans input to the UNION operator. The handling of Multi-block queries will not be further discussed here. However, a notion of equivalence can be easily arrived at for the UNION queries by restricting attention to UNION queries that operate on identical plans. Technique for Identifying Equivalence In this section, an efficient technique for identifying equivalent sub-plans in a plan generated by the query optimizer 306 is described. The technique makes use of the notion of equivalence (.about.) introduced in the previous section. It is a tree traversal that identifies equivalence classes. An example of the technique Equivalence Class Generation follows. This technique is based on a level-by-level walk of the plan tree generated by the query optimizer 306, starting with the leaf level, and identifying the nodes which are equivalent at that level, and using this information to identify equivalent nodes at the next level and so on. A query plan Tree T is input to the query optimizer 306. The equivalence class of nodes in T with respect to (.about.) is the output of the query. Begin cur_node=left most leaf; lvl=0 While (cur_node!=root) while there are no more nodes at level lvl for each unmarked node n at level lvl if (cur_node.about.n) add_node_to_eq_class (lvl, cur_node, n) // adds node n to the equiv_class[lvl][cur_node] mark (cur_node); mark (n) cur_node=next unmarked node at level lvl; lvl=lvl+1; cur_node=leftmost node at level lvl; end The above technique requires a pass of each node exactly once and hence has a cost that is linear in the number of nodes in the plan tree. FIG. 4 illustrates a query plan along with the equivalence classes identified by the technique. The nodes representing the same equivalence class are shaded. Cost Considerations for Materializing Transient-Views The first phase of the technique may generate several equivalence classes. The members of each equivalence class may contain several sub-plans that are similar. A materialized view can be used to answer the queries representing the sub-plans in each equivalence class. The materialized view contains the union of the results of all the sub-plans. The results produced by each sub-plan can be obtained by applying filters to the materialized view. For each equivalence class it has to be decided whether or not to use the materialized view. A cost model is used to determine whether the equivalence class will improve performance to materialize the transient-view. The steps taken to determine whether to materialize a transient-view are discussed below. Initially, the set of equivalence classes are pruned, so that temporary tables are not unnecessarily created. Once the set of equivalence classes are pruned, two problems must be solved. First, the properties for the views to be materialized are determined for each equivalence class, and a query execution plan is generated that represents the union of the results of the queries in that sub-plan. Second, it is determined whether the performance will improve if this view is materialized. These steps are discussed in detail in the following paragraphs. The discussion of the different equivalence pruning techniques is postponed to the end of this section, since it is important to understand how the materialized views are generated. The technique for determining the query execution plan and cost for the materialized view is described first. Transient-View Plan Generation Each sub-plan in an equivalence class is represented by a set of properties. These properties are summarized in Table 1. To determine whether to materialize a view for an equivalence class, the properties of the transient-view are first determined, an optimal plan for the view is generated, and the plans for filtering the results of the view for each sub-plan in the equivalence class. The property description of each sub-plan in an equivalence class is used to generate a property list that corresponds to the plan which generates the union of the results of the sub-plans in that class. The plan that corresponds to the union of the results of the sub-plans in a class is referred to as the "super-sub-plan". Table 7 shows the combined properties of a view that generates the union of the results of two sub-plans in an equivalence class.
TABLE 7
Plan Properties
View
Property Notation Property
Tables in the plan T.sub.view T.sub.i
Columns selected Cols.sub.view Cols.sub.1.orgate.Col
S.sub.2
Join predicates J P.sub.view J P.sub.i
Selection predicates S P.sub.view S P.sub.1 OR S
P.sub.2
Aggregation Functions A F.sub.view AF.sub.1 (Exp) .orgate.
AF.sub.2 (Exp)
Columns in the Gc.sub.view GC.sub.1.orgate.GC.sub.2
group by list .orgate.Addnl.sub.i
Data source S.sub.view S.sub.i
plan executes
Cost of executing plan Cost.sub.view To be
determined
Number of result rows Card.sub.view To be
determined
The list of properties and the description of how to combine them and generate a property list for the transient-view is discussed below. Tables: The sub-plans in an equivalence class have the exact same tables, therefore the tables in the transient-view have the same tables represented here by T.sub.i. Columns: The columns in the SELECT list is the union of the columns in the two sub-plans. Join Predicates: The join predicates in two sub-plans in all equivalence class are identical by definition. Therefore, the join predicate of one sub-plan is used. Predicates: SP.sub.i is the representation of conjuncts of simple predicates of the form Col RelOp value in the two plans. The predicate property of the combined plan, SP.sub.view. is obtained by ORing SP.sub.1 and SP.sub.2. If either SP.sub.1 or SP.sub.2 is null, then the predicate property of the combined plan is also null. The combined predicate is then optimized by applying standard predicate optimization techniques, to remove redundancy, and merge predicates. Aggregation Function: The aggregation function is the union of the aggregation functions of the two plans. If two aggregation functions are identical, one of the functions can be removed. Group By List: The group by list by definition should be a superset of the columns in the SELECT list. The group by list of the combined plan is the union of the group by list of the two sub-plans. Duplicate columns are removed from the group by list. Data Source: The data source that the query corresponding to the plan executes on is the same. The plan properties generated for a view representing two sub-plans can be extended to apply to a third sub-plan and so on until the plan property for the transient view representing all sub-plans in the equivalence class is obtained. The property information of the transient view does not contain the cost and the cardinality information. In order to get this information, the query that represents the transient view is first generated from the property list of the transient view. This query is shown below: SELECT COlS.sub.view, Af.sub.view (Exp) FROM T.sub.view WHERE JP.sub.view AND SP.sub.view GROUP BY GC.sub.view, The query is then optimized, and the execution plan, the cost, and cardinality information is obtained for the transient view. The result of the transient view contains data needed by all the sub-plans in the equivalence class. It is important to note that only the portion of the query representing the transient-view is optimized and not the entire query. Filter Plans The results generated by the query plan representing the transient views contains data that is the union of the results of the sub-plan belonging to the equivalence class. Therefore, appropriate filter plans need to be applied to obtain the results required for each sub-plan. In order to do this, filter queries are defined for each sub-plan in the equivalence class. The filter query for each sub-plan in an equivalence class is defined based on the transient-view and the properties of the sub-plan. The filter query is defined below: SELECT Cols.sub.i, AF.sub.i (Exp) FROM MATVIEW WHERE SP.sub.i GROUP BY GC.sub.i The Cost Based Optimizer 112 is used to generate plans for the filter query for each sub-plan in the equivalence class. This is necessary for two reasons. First, the plan information is needed to generate executable code for the filters. Second, the cost information of the filter plan is needed to determine if it is efficient to use transient-views to optimize the query. The cost property of the filter operations for each sub-plan is represented as FilterCost.sub.i. Cost and Cardinality Information An optimizer cost model is used to decide whether it would be beneficial to materialize a view. The cost of executing the sub-plans in the equivalence class is compared to the cost of materializing a "super-sub-plan" and answering the queries represented by each sub-plan by applying a filter on top of the materialized view. The following equation represents the comparison. ##EQU1## If the cost of materializing the view and applying the filters is less than the cost of executing the sub-plan, the view is materialized. FIG. 7 is a flow diagram illustrating the steps performed by the Cost Based Optimizer 112 to identify execution steps for efficient query processing. In Block 700, the Cost Based Optimizer 112 identifies redundancies in an original query's execution steps. In Block 702, the Cost Based Optimizer 112 creates a new set of equivalent execution steps by eliminating redundancies. In Block 704, the Cost Based Optimizer 112 estimates the cost of the original query's execution steps. In Block 706, the Cost Based Optimizer 112 estimates the cost of the equivalent execution steps. In Block 708, based on the cost determinations, the Cost Based Optimizer 112 determines whether the original query's execution steps or the equivalent execution steps are to be used for efficient query processing. Equivalence Class Pruning The first phase of the technique may generate several equivalence classes at each level. The classes at the first level contain single table sub-plans. At the second level, the sub-plans in the equivalence class, at higher levels, are based on the presence of smaller equivalent sub-plans at lower levels. Since the equivalence classes at higher levels contain sub-plans that overlap, it may not be possible to fully utilize the performance improvement, if all the equivalence classes are materialized. In this example, all equivalence classes generated by the first stage are selected. This could result in sub-optimal plan. FIG. 4 shows an exemplary plan 400 generated by the Query Optimizer 306, and set of equivalence classes generated by the first phase of the technique. FIG. 4 shows twelve nodes, N1 through N12. The Nodes belonging to the same equivalence class are shaded with the same color. The nodes that are in the same equivalence class are: Level 1: EQ1.1: {N1, N3}, EQ1.2: {N2, N4, N5), EQ1.3: N5; Level 2: EQ2.1{N6, N7}, EQ2.2{N8); and Level 3: EQ2.3{N9, N10}. For this query there are three equivalence classes at level 1. The equivalence class EQ2.1 at level 2 contains two JOIN operators that operate on the members of the level 1 equivalence class. At the third level EQ2.3 has two group by nodes. If views are materialized for all the equivalence class, the resulting plan 500 may not improve performance, as represented by FIG. 5. In FIG. 5, the materialized views for EQ1.1 502, which does not contribute to improving the performance, are unnecessarily generated. EQ.1.1 is not represented in the new plan 500. However, the views for EQ.1.2 504 and the views for EQ2.3 506 may improve performance. The pruning technique starts by selecting those equivalence classes at the highest level that have more than one node. This ensures that those equivalence classes are chosen which have nodes that share a lot of work in common. The Cost Based Optimizer 112 is used to determine whether the plan can be improved by using the equivalence class at the highest level. If it is determined that performance cannot be improved, they are removed from the selected list, otherwise they are added to the selected set. For equivalence classes at each level, the nodes are checked to determine if any of the nodes that are members of the equivalence class are the children of the nodes in the equivalence classes already selected. If all the members are present in the classes selected earlier, this equivalence class is pruned, otherwise, the cost of the effect of using this class to optimize the plan is determined and the class is added to the selected list of equivalence classes. This enables selection of a non-overlapping set of equivalence classes. When there are equivalence classes that overlap, the pruning technique checks to determine whether all the members in the class are accounted for by equivalence classes at higher levels. This ensures that no optimization opportunities are missed. Also, equivalence classes that could potentially reduce the benefit of sharing computations are not materialized. FIG. 6 shows the new plan 600 that is generated when the pruning technique is used to prune the set of equivalence classes. It avoids materializing the sub-plan for the equivalence class EQ1.1 502. However, both EQ1.2 504 and EQ2.3 506 are a part of the new plan 600. Scalability of the Cost Based Optimizer One of the important problems in the area of answering queries using views is the following: Given a set of queries that are most often posed against a database, what is the correct set of views that should be materialized in order to answer queries efficiently? The transient-view based optimization technique can be applied in the context of this view selection problem in the following manner. Given a set of queries or, equivalently, a set of plans corresponding to the queries, the Cost Based Optimizer's 112 technique for generating the transient view can identify the portions of the queries that are redundantly computed and recommend the transient view that should be materialized in order to improve performance. That is, given a set of queries, the Cost Based Optimizer 112 can generate a "generic" view (i.e., a "generic" set of execution steps) that can be used by each of the queries in the set or by a new query. In the context of the view selection problem, the views the Cost Based Optimizer 112 recommends would essentially be the views that should be materialized. Thus, the Cost Based Optimizer 112 can be leveraged to build a system that, given a set of queries, will recommend the set of views to be materialized for optimum query performance. FIG. 8 is a flow diagram illustrating the steps performed by the Cost Based Optimizer 112 to enable scalability. In Block 800, the Cost Based Optimizer 112 receives a set of queries. In Block 802, the Cost Based Optimizer 112 identifies a generic view for the received set of queries. In Block 804, the Cost Based Optimizer 112 determines, for any query, whether the query can be processed using the generic view, and, if the query can be processed using the generic view, the Cost Based Optimizer 112 processes the query using the generic view. Performance The Cost Based Optimizer 112 for using transient views to optimize queries was implemented in DataJoiner [ea97], a heterogeneous commercial relational database system based on DB2. The TPCD benchmark queries were used to evaluate the performance impact of using transient views. Two additional queries based on the TPCD benchmark schema were also formulated. The benchmark queries were evaluated on a one processor RS6000 machine and on an AIX 3.2 platform, running DataJoiner. Each query was ran 10 times, when the machines were idle (both the local and remote database) and reported the average of the execution times. The following paragraphs discuss the performance of the Cost Based Optimizer 112. First, the TPCD schema is briefly described. Following this, the queries that were used to evaluate performance are described. Finally, the performance of the three techniques that were used to prune the equivalence classes is described. TPCD Benchmark Schema The schema for the TPCD benchmark consists of a PART(20000) table and SUPPLIER(1000) table for suppliers who supply parts. The information of the SUPPLIER-PART relationship is maintained in the PARTSUPP (80000) table. Information regarding customers is in a CUSTOMER(15000) table. Status information for orders placed by customers is maintained in the ORDER table. The key in the ORDER(150000) table is used to identify the parts and the suppliers from whom the part is ordered. This information is in a LINEITEM table, that also maintains shipping information, price, quantity ordered and discount. The ORDER table also maintains the total price of the order, the order and ship priorities. Small NATION(25) and REGION(5) tables were used to associate suppliers and customers with the area they come from. For further information on the TPCD benchmark refer to the TPCD benchmark specification [TPC93]. The overall database size was around 100 MB. The TPCD tables were split and the SUPPLIER, NATION, and REGION table were placed on a remote database that was running on an AIX RS6000 machine that was accessed over the network. The rest of the tables were placed in the local DataJoiner database. DataJoiner accesses the remote tables through a user defined alias, eg: for SUPPLIER the alias is REMDB_SUPPLIER as though these were local tables. Queries to Evaluate Performance Three queries, query 2, query 11, and query 15, were chosen from the TPCD benchmark suite. These three queries were chosen because, casual observation of the three queries suggest that these three queries have redundant computation, and employing transient views may be beneficial for their execution. The performance of the rest of the TPCD benchmark queries (query 1 through query 17) were also evaluated to identify transient views. The Cost Based Optimizer 112 did not detect any redundancy in computation and the plans of these queries remained unchanged. The execution times of these queries also did not change, indicating that the Cost Based Optimizer 112 detected transient views that did not affect normal query processing. The queries are briefly described below. The detailed syntax of the queries are in TABLE 8. TPCD Q02: Find in a given region, for each part of a certain type and size, the supplier who can supply it at minimum cost. If several suppliers in that region offer the desired part type and size at the same (minimum) cost, the query lists the parts from the suppliers with the 100 highest account balances. For each supplier, the query lists the supplier's account balance, name, nation, the parts number and manufacturer, the supplier's address, phone number and comment information. TPCD Q11: This query finds by scanning the available stock of suppliers in a given nation, all the parts that represent a significant percentage of the total value of all available parts. The query displays the part number and the value of those parts in descending order of value. TPCD Q15: Finds all the suppliers who contributed the most to the overall revenue for parts shipped during a given quarter of a year. Query NQ1: Find the parts, whose size is 45 that represents a significant percentage of the value of the parts that are of size 48. Query NQ2: Print the names of those parts that were given a 10% discount and also taxed 10% that have been returned and also not accepted. Optimized Plan vs Transient Views First, the performance of transient views on the three TPCD queries is evaluated and compared with the cases in which the Cost Based Optimizer 112 is not used. FIG. 9 shows a graph of the performance comparisons for these two cases. The results show that transient views reduce the execution time for queries Q11 and Q15 in half. The execution time for Q02 does not change since the transient-view detection mechanism does not detect any redundancy in the plan, although the description of the query indicates that there is redundancy in the plan. This will be better understood in the next section where the transient-view performance is compared with that of identifying common sub-expression based on query syntax. FIG. 10 shows a graph of the performance of two queries that were formulated to further illustrate the performance benefits of using transient-views. Similar to the TPCD queries, the performance graph show the tremendous improvement in performance when transient views are used. For example, the transient views significantly reduce the execution time for queries NQ1 and NQ2. Transient View vs Ouerv Rewrite In this section, the detrimental effect of using a query rewrite mechanism to identify common sub-expressions in a query by examining the query syntax as in [Ha174]. The performance of TPCD-Q02 when transient views were used to optimize the query was compared to optimizing the query through a query rewrite mechanism that identifies common sub-expressions. TABLE 8 shows the syntax of the query. When examining the plan of the query, it was observed that the sub-plan that can be factored is very small, since it is optimal to join the PART table with PARTSUPP. The cost of executing the query is shown in FIG. 11 is at approximately 40 seconds for the Q02 query. The transient view technique identifies the sub-plan factor that is a join between the REGION and NATION tables. Since the cost of executing the sub-plan is very small, materializing the transient view does not improve performance and the execution cost remained at 4 seconds. The query rewrite optimization identifies the join between PARTSUPP, REGION, SUPPLIER, and NATION as a common sub-expression. This reduces the join enumeration choices for the optimizer. The optimizer cannot join the PART table with the PARTSUPP table and make use of the index on PARTSUPP table. The performance of query execution is significantly worse. The execution time is around 10 times worse when the common sub-expression is used. This demonstrates that identifying common sub-expression from the query syntax can degrade performance significantly, while using the technique of factoring sub-plans from the plan helps in improving performance when possible. SUMMARY OF RESULTS In summary, the code has no impact on performance for queries that do not benefit from transient views. The overhead of the technique to detect transient views is negligible. Detecting and utilizing transient views help improve performance tremendously demonstrated by the reduction in half of the execution time of the two TPCD benchmark queries. The reason for this reduction is due to using transient view to avoid re-computing the results of a large sub-plan. If the sub-plan results are used multiple times within the same query, the performance benefits would be greater. Comparison of employing transient view technique with that of identifying common sub-expressions based on the query syntax shows that a query rewrite mechanism limits the optimizers choices in choosing plans and could lead to plans that severely degrade performance. This demonstrates that generating transient-views from an optimal plan results in improved performance, and it does not affect queries that do not benefit from transient views. CONCLUSION This concludes the description of the preferred embodiment of the invention. The following describes some alternative embodiments for accomplishing the Cost Based Optimizer 112. For example, any type of computer, such as a mainframe, minicomputer, or personal computer, or computer configuration, such as a timesharing mainframe, local area network, or standalone personal computer, could be used with embodiments of the Cost Based Optimizer 112. 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. TPCD Queries TPCD-Q02: Find in a given region, for each part of a certain type and size, the supplier who can supply it at minimum cost. If several suppliers in that region offer the desired part type and size at the same (minimum) cost, the query lists the parts from the suppliers with the 100 highest account balances. For each supplier, the query lists the supplier's account balance, name, nation, the parts number and manufacturer, the supplier's address, phone number and comment information.
SELECT S_ACCTBAL, S_NAME, N_NAME, P_PARTKEY,
P_MFGR, S_ADDRESS, S_PHONE, S_COMMENT
FROM PART P, REMDB_SUPPLIER S, PARTSUPP PS,
REMDB_NATION, REMDB_REGION
WHERE P_PARTKEY = PS_PARTKEY
AND P_SIZE = 15
AND P_TYPE LIKE `%BRASS%`
AND S_SUPPKEY = PS_SUPPKEY
AND S_NATIONKEY = N_NATIONKEY
AND N_REGIONKEY = R_REGIONKEY
AND R_NAME = `EUROPE`
AND PS_SUPPLYCOST = (SELECT MIN(PS_SUPPLYCOST)
FROM PARTSUPP PS1, REMDB_SUPPLIER S1,
REMDB_NATION N1,
REMDB_REGION
R1 WHERE P.P_PARTKEY = PS1.PS_PARTKEY
AND S1.S_SUPPKEY PS1.PS_SUPPKEY
AND S1.S_NATIONKEY =
N1.N_NATIONKEY AND N1.N_REGIONKEY =
R1.R_REGIONKEY AND R1.R_NAME = `EUROPE`)
ORDER BY S_ACCTBAL DESC, N_NAME, S_NAME,
P_PARTKEY;
TPCD_Q11: This query finds by scanning the available stock of suppliers in a given nation, all the parts that represent a significant percentage of the total value of all available parts. The query displays the part number and the value of those parts in descending order of value.
SELECT
PS_PARTKEY,
SUM(PS_SUPPLYCOST*PS_AVAILQTY)
FROM PARTSUPP, REMDB_SUPPLIER, REMDB_NATION
WHERE PS_SUPPKEY = S_SUPPKEY
AND S_NATIONKEY = S_SUPPKEY
AND N_NAME = `GERMANY`
GROUP BY PS_PARTKEY
HAVING SUM(PS_SUPPLYCOST*PS_AVAILQTY)>
(SELECT SUM(PS_SUPPLYCOST*PS_AVAILQTY)*0.001
FROM PARTSUPP, REMDB_SUPPLIER,
REMDB_NATION WHERE PS_SUPPKEY = S_SUPPKEY
AND S_NATIONKEY = N_NATIONKEY
AND N_NAME = `GERMANY`)
ORDER BY 2 DESC;
.cndot. TPCD_Q15: Finds all the suppliers who contributed the most
to the overall revenue for parts shipped during a given quarter of a year.
SELECT S_SUPPKEY, S_NAME, S_ADDRESS, S_PHONE,
TOTAL_REVENUE
FROM REMDB_SUPPLIER, (SELECT L_SUPPKEY AS
SUPPLIER_NO,
SUM(L_EXTENDEDPRICE * (1-L_DISCOUNT)) AS
TOTAL_REVENUE
FROM LINEITEM
WHERE L_SHIPDATE>=DATE(`1996-01-01`)
AND L_SHIPDATE <DATE(`1996-01-01`) + 3 MONTHS
GROUP BY L_SUPPKEY)R
WHERE S_SUPPKEY = R.SUPPLIER_NO
AND R.TOTAL_REVENUE =
(SELECT MAX(R1.TOTAL_REVENUE)
FROM (SELECT L_SUPPKEY AS SUPPLIER_NO,
SUM(L_EXTENDEDPRICE *
(1-L_DISCOUNT)) AS TOTAL_REVENUE
FROM LINEITEM
WHERE L_SHIPDATE>=DATE(`1996-01-01`)
AND L_SHIPDATE<DATE(`1996-01-01`) + 3 MONTHS
GROUP BY L_SUPPKEY) R1);
.cndot. TPCD_NQ1: Find the parts, whose size is 45 that
represents a significant percentage of the value of the parts that
are of size 48
SELECT SUM(PS_SUPPLYCOST*PS_AVAILQTY),
PS_PARTKEY, P_NAME
FROM PARTSUPP, REMDB_SUPPLIER, PART, LINEITEM
WHERE PS_SUPPKEY = S_SUPPKEY
AND P_PARTKEY = PS_PARTKEY
AND L_PARTKEY = P_PARTKEY
AND P_SIZE = 45
GROUP BY PS_PARTKEY, P_NAME
HAVING SUM(PS_SUPPLYCOST*PS_AVAILQTY)>
(SELECT SUM(PS_SUPPLYCOST*PS_AVAILQTY) * 0.0001
FROM PARTSUPP, REMDB_SUPPLIER, PART, LINEITEM
WHERE PS_SUPPKEY = S_SUPPKEY
AND P_PARTKEY = PS_PARTKEY
AND L_PARTKEY = P_PARTKEY
AND P_SIZE = 48)
ORDER BY 2 DESC;
TPCD_NQ2: Print the names of those parts that were given a 10% discount and also taxed 10% that have been returned and also not accepted.
CREATE NOTACCEPTED (PARTKEY, RETURN) AS
(SELECT L_PARTKEY, L_RETURNFLAG
FROM LINEITEM
WHERE L_RETURNFLAG=`N`
AND L_TAX=0.01
AND L_DISCOUNT=0.01);
CREATE VIEW RETURNED (PARTKEY, RETURN) AS
(SELECT L_PARTKEY, L_RETURNFLAG
FROM LINEITEM
WHERE L_RETURNFLAG=`R`
AND L_TAX=0.01
AND L_DISCOUNT=0.01);
SELECT REJECT.PARTKEY, PART.P_NAME
FROM RETURNED, REFUSED, PART
WHERE NOTACCEPTED.PARTKEY=RETURNED.PARTKEY
AND PART.PARTKEY=RETURNED.PARTKEY;
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