Abstract:
In an optimizer within a Relational Database Management System improved ways in which a search space (the universe of possible join combinations) is generated and managed and improved ways in which the elements of a search space are evaluated so that among other things unpromising elements are efficiently dropped (pruned).

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to information processing environments. More particularly, the present invention relates to capabilities that enhance substantially the operation, effectiveness, efficiency, etc. of query optimizers that are found in Database Management Systems (DBMSs). 
     2. Background Art 
     A common element of an information processing environment is a database, which is in effect a computer-based repository of information. Databases are extraordinarily prevalent and may be found on almost any computing platform including inter alia mainframe computers; computer servers; Personal Computers (PCs); handheld computers; pagers; Personal Digital Assistants (PDAs); cellular telephones, smart phones, and other wireless devices; radios; TVs; navigation systems; automobile audio systems; net appliances; etc. 
     A DBMS serves as a something of a ‘bridge’ between the information in a database (handling inter alia the organization of the information, the storage of the information on different devices, etc.) and users of the database. Among other things a DBMS provides database users with a logical or conceptual view of a database, allowing them to not concern themselves with inter alia the physical, implementation, etc. particulars of the database. When a user wishes to perform some action on the database (e.g., to retrieve a piece of information from the database, to update a piece of information in the database, to add a new piece of information to the database, etc.) the user will typically submit a query to the DBMS. 
     A database may be organized according to different models such as hierarchical, network, and relational. 
     Under a relational model a database may comprise inter alia one or more tables (relations), each table comprising one or more rows or records (tuples), each row/record comprising one or more columns or fields (attributes), with each column/field comprising some piece of information. As an example, a database comprising information on an organization&#39;s employees might contain a table EMPLOYEES that houses one record for each employee. Each record in the EMPLOYEES table might contain fields that preserve specifics about the employee such as inter alia the employee&#39;s name (e.g., a field named EMP_NAME), home address (e.g., a field named EMP_ADDRESS), current position, salary, work telephone number, etc. 
     Under a relational model a ‘bridge’ DBMS takes the form of a Relational DBMS (RDBMS) and a query to a RDBMS typically takes the form of a Structured Query Language (SQL) statement. 
     A SQL statement (such as for example ‘SELECT EMP_NAME, EMP_ADDRESS FROM EMPLOYEES’) expresses a desired result (in the instant example, ‘please return to me the name and the address of each employee’) but does not inter alia identify how those results should be obtained. In other words, the query itself does not specify how the query should be evaluated by an RDBMS. A component of an RDBMS, a query optimizer or optimizer, is responsible for inter alia (1) identifying the different valid ways in which (plans for how) the data within the database may be accessed so as to achieve the result that is requested by a SQL statement, (2) evaluating and costing the identified plans, and (3) selecting the ‘best’ (e.g., the cheapest, the fastest, etc.) plan. 
     As it completes its work a query optimizer may identify and evaluate a number of items, artifacts, criteria, etc. including inter alia join operations. 
     Classically a RDBMS supports dyadic join operations, that is join operations that involve just two entities such as tables (e.g., the join operation T 1               T 2  involving the two tables T 1  and T 2 ). Consequently for a query that requires an n-way join (i.e., a join operation that involves n tables where n&gt;2) a query optimizer must inter alia enumerate or identify (possibly just some subset of) the universe of possible join combinations (i.e., a search space); evaluate, based on various criteria including for example cost, some or all of the candidates in the search space; and then string together one specific sequence of individual two-way join operations to arrive at the ‘best’ (e.g., perhaps the cheapest) way of realizing the required n-way join. For example, for a four-way join involving four tables (T 1 , T 2 , T 3  and T 4 ) a query optimizer might arrive at the specific join sequence ((T 1             T 2 )           (T 3             T 4 )).
     Conventional query optimization techniques often give rise to various disadvantages. For example: 
     1) As the number of entities (e.g., tables) in an n-way join increases the size of the resulting search space, that is the universe of possible join combinations, grows very quickly resulting in inter alia longer and longer amounts of time to iterate through the elements of the search space (to for example access, review, cost, etc. those elements). 
     2) For many dynamically generated queries the execution time of the query itself may be quite small but the optimization time may be quite large and thus disproportionate to the execution time. 
     From all of the different plans that an optimizer may have to chose from, if it selects a ‘good’ plan then processing of the query will be completed ‘quickly’ (with possibly inter alia lower system resource consumption, etc.). Alternatively, if it selects a ‘bad’ plan then processing of the query will be completed ‘slowly’ (with possibly inter alia higher system resource consumption, etc.). 
     Given the performance, system resource consumption, etc. ramifications and implications of the query optimization process it is obviously very important for an optimizer to identify and select the ‘best’ available query execution plan. That objective—identifying and selecting the ‘best’ available query execution plan—is made challenging by the host of constraints that an optimizer must operate under including inter alia available system resources (such as memory), specific query characteristics, parameters such as the maximum amount of time that an optimizer may spend on any particular activity, the status of the RDBMS, etc. 
     Aspects of the present invention address the challenge that was noted above (1) by (a) improving upon the way in which a search space is generated and managed and (b) improving on the way in which the elements of a search space are evaluated so that among other things unpromising elements are efficiently dropped (pruned) (2) while addressing, in new and innovatory ways, various of the not insubstantial challenges that are associated with same. 
     SUMMARY OF THE INVENTION 
     In one embodiment of the present invention there is provided a server-based method for enhanced query optimizer search space management comprising (1) saving, uncosted and in an ordered fashion, a subset of the enumerated partitions that are generated by a join enumeration algorithm in a memoization construct, (2) generating a plan and costing the plan for a subset of the saved partitions, such that unpromising partitions are pruned, and (3) selecting one of the costed plans. 
     Further features and advantages of the present invention, as well as the structure and operation of various embodiments thereof, are described in detail below with reference to the accompanying drawings. It is noted that the invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts an exemplary computer system through which embodiments of aspects of the present invention may be implemented. 
         FIG. 2  illustrates an exemplary computer software environment that may among other things direct the operation of aspects of  FIG. 1 &#39;s computer system. 
         FIG. 3  illustrates aspects of an exemplary information processing environment. 
         FIG. 4  illustrates an ordered-Par( ) algorithm that encapsulates aspects of the present invention. 
         FIG. 5  illustrates one possible EnumeratePartition( ) algorithm. 
         FIG. 6  illustrates one possible GenerateBestPlan( ) algorithm. 
         FIG. 7  captures the results of a particular query being optimized through two different algorithms. 
         FIG. 8  captures two specific results from a particular query being optimized through two different algorithms. 
         FIGS. 9 → 11  capture two specific results from a particular query having three different shapes being optimized through different algorithms. 
     
    
    
     The features and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the above identified drawings. 
     Throughout the drawings (a) like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements and (b) the left-most digit(s) of a reference number generally identify the drawing in which the reference number first appears. For example, in  FIG. 6  reference numeral  504  would direct the reader to  FIG. 5  for the first appearance of that item. 
     It will be understood that the drawings identified above depict embodiments of the invention. Variations of these embodiments will be readily apparent to persons skilled in the relevant art(s) based on the teachings contained herein. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention are described herein in the context of a method and apparatus for enhanced query optimizer search space ordering. Those of ordinary skill in the relevant art will realize that the following detailed description of the present invention is illustrative only and is not intended to be in any way limiting. Other embodiments of the present invention will readily suggest themselves to such skilled persons having the benefit of this disclosure. Reference will now be made in detail to implementations of the present invention as illustrated in the accompanying drawings and as described below. 
     In the interest of clarity, not all of the routine features of the implementations described herein are shown and described. It will, of course, be appreciated that in the development of any such actual implementation, numerous implementation-specific decisions must be made in order to achieve the developer&#39;s specific goals, such as compliance with application- and business-related constraints, and that these specific goals will vary from one implementation to another and from one developer to another. Moreover, it will be appreciated that such a development effort might be complex and time-consuming, but would nevertheless be a routine undertaking of engineering for those of ordinary skill in the art having the benefit of this disclosure. 
     Various aspects of the present invention may be implemented by software, firmware, hardware, or any combination thereof.  FIG. 1  illustrates an example computer system  100  in which the present invention or portions thereof (such as for example described below in accordance with  FIGS. 3-11  and their corresponding description can be implemented as computer-readable code. Various embodiments of the invention are described in terms of this example computer system  100 . After reading this description, it will become apparent to a person skilled in the relevant art how to implement the invention using other computer systems and/or computer architectures. 
     Computer system  100  includes one or more processors, such as processor  104 . Processor  104  can be a special purpose processor or a general purpose processor. Processor  104  is connected to a communication infrastructure  102  (for example, a bus or a network). 
     Computer system  100  also includes a main memory  106 , preferably Random Access Memory (RAM), containing possibly inter alia computer software and/or data  108 . 
     Computer system  100  may also include a secondary memory  110 . Secondary memory  110  may include, for example, a hard disk drive  112 , a removable storage drive  114 , a memory stick, etc. A removable storage drive  114  may comprise a floppy disk drive, a magnetic tape drive, an optical disk drive, a flash memory, or the like. A removable storage drive  114  reads from and/or writes to a removable storage unit  116  in a well known manner. A removable storage unit  116  may comprise a floppy disk, magnetic tape, optical disk, etc. which is read by and written to by removable storage drive  114 . As will be appreciated by persons skilled in the relevant art(s) removable storage unit  116  includes a computer usable storage medium  118  having stored therein possibly inter alia computer software and/or data  120 . 
     In alternative implementations, secondary memory  110  may include other similar means for allowing computer programs or other instructions to be loaded into computer system  100 . Such means may include, for example, a removable storage unit  124  and an interface  122 . Examples of such means may include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an Erasable Programmable Read-Only Memory [EPROM], or Programmable Read-Only Memory [PROM]) and associated socket, and other removable storage units  124  and interfaces  122  which allow computer software and/or data to be transferred from the removable storage unit  124  to computer system  100 . 
     Computer system  100  may also include an input interface  126  and a range of input devices  128  such as, possibly inter alia, a keyboard, a mouse, a track ball, a pointing device, etc. 
     Computer system  100  may also include an output interface  130  and a range of output devices  132  such as, possibly inter alia, a display monitor, one or more speakers, a printer, etc. 
     Computer system  100  may also include a communications interface  134 . Communications interface  134  allows computer software and/or data  138  to be transferred between computer system  100  and external devices. Communications interface  134  may include inter alia a modem, a network interface (such as inter alia an Ethernet card), a communications port, a Personal Computer Memory Card International Association (PCMCIA) slot and card, or the like. Computer software and/or data  138  transferred via communications interface  134  are in the form of signals  136  which may be electronic, electromagnetic, optical, or other signals capable of being received by communications interface  134 . These signals  136  are provided to communications interface  134  via a communications path  140 . Communications path  140  carries signals and may be implemented using wire or cable, fiber optics, a phone line, a cellular phone link, a Radio Frequency (RF) link or other communications channels. 
     As used in this document, the terms “computer program medium,” “computer usable medium,” and “computer readable medium” generally refer to media such as removable storage unit  116 , removable storage unit  124 , and a hard disk installed in hard disk drive  112 . Signals carried over communications path  140  can also embody the logic described herein. Computer program medium and computer usable medium can also refer to memories, such as main memory  106  and secondary memory  110 , which can be memory semiconductors (e.g. Dynamic Random Access Memory [DRAM] elements, etc.). These computer program products are means for providing computer software to computer system  100 . 
     Computer programs or software (also called computer control logic) are stored in main memory  106  and/or secondary memory  110 . Computer programs may also be received via communications interface  134 . Such computer programs, when executed, enable computer system  100  to implement the present invention as discussed herein. In particular, the computer programs, when executed, enable processor  104  to implement the processes of aspects of the present invention, such as for example the steps discussed below in accordance with  FIGS. 3-11  and their corresponding description. Accordingly, such computer programs represent controllers of the computer system  100 . Where the invention is implemented using computer software, the computer software may be stored in a computer program product and loaded into computer system  100  using inter alia a removable storage drive  114 , an interface  122 , a hard drive  112  or a communications interface  134 . 
     The invention is also directed to computer program products comprising computer software stored on any computer usable medium. Such computer software, when executed in one or more data processing devices, causes the data processing device(s) to operate as described herein. Embodiments of the invention employ any computer usable or readable medium, known now or in the future. Examples of computer usable mediums include, but are not limited to, primary storage devices (e.g., any type of RAM), secondary storage devices (e.g., hard drives, floppy disks, Compact Disc Read-Only Memory [CD-ROM] disks, Zip disks, tapes, magnetic storage devices, optical storage devices, Microelectromechanical Systems [MEMS], nanotechnological storage device, etc.), and communication mediums (e.g., wired and wireless communications networks, local area networks, wide area networks, intranets, etc.). 
     When it is used within a (Local Area Network (LAN), Wide Area Network (WAN), etc.) networking environment computer system  100  may be connected (by inter alia a wired connection or a wireless connection) to a network through a network interface or adapter (such as inter alia an Ethernet card) via communications interface  134 . Under such a networked environment, computer programs (computer control logic) may be stored, either in whole or in part, on one or more remote memory storage devices (in addition to the previously noted main memory  106  and/or secondary memory  110 ). 
       FIG. 2  illustrates a computer software environment  200  that inter alia may direct the operation of aspects of the computer system  100 . Computer software environment  200 , which may be stored inter alia in main memory (e.g., RAM)  106  and/or on secondary storage (e.g., a hard disk drive)  110 , includes inter alia an Operating System (OS)  204 . The OS  204  manages low-level aspects of computer operation including inter alia managing the execution of processes, memory allocation, file Input and/or Output (I/O), and device I/O. One or more application programs, such as client application software or programs  202  (e.g.,  202   a ,  202   b,  . . .  202   n ) may be loaded (e.g., transferred from storage  110  into main memory  106 ) for execution by the computer system  100 . The applications or other software intended for use on the computer system  100  may also be stored as a set of downloadable computer-executable instructions, for example, for downloading and installation from an Internet location (e.g., an application server, World Wide Web (WWW) server, etc.). 
     Computer software environment  200  includes inter alia a Graphical User Interface (GUI)  206  for receiving user commands and data in a graphical (e.g., a point-and-click) fashion. These inputs, in turn, may be acted upon by the computer system  100  in accordance with instructions from the OS  204  and/or client application software  202 . The GUI  206  also serves to display the results of operation from the OS  204  and client application software  202 , whereupon the user may supply additional inputs or terminate the session. Commonly the OS  204  operates in conjunction with possibly inter alia device drivers  208  and the system Basic Input/Output System (BIOS)  210 , particularly when interfacing with peripheral devices  212 . 
     Popular examples of OS  204  include inter alia the different versions of Windows from Microsoft®, the different versions of UNIX, the different versions of Linux, etc. 
     The above-described computer system and computer software environment were presented for purposes of illustrating the basic underlying PC, server, etc. computer components that may be employed for implementing aspects of the present invention. It will be readily apparent to one of ordinary skill in the relevant art that numerous other components and/or component arrangements are easily possible. 
     For simplicity of exposition the description below will at times present examples in which it will be assumed that there exists a “server” (e.g., an application server, a WWW server, etc.) that inter alia communicates with one or more “clients” (e.g., PCs; PDAs; handheld computers; cellular telephones, smart phones, and other wireless devices; etc.). The present invention, however, is not limited to any specific environment or device configuration. For example, a client/server distinction is not necessary to the invention but is used to provide a framework for discussion. To the contrary, the present invention may be implemented in any type of information processing environment that is capable of supporting the methodologies of the present invention as described in detail below. 
       FIG. 3  and reference numeral  300  illustrate aspects of an information processing environment comprising among other things one or more clients  302  (which may include inter alia PCs; handheld computers; pagers; PDAs; cellular telephones, smart phones, and other wireless devices; radios; TVs; navigation systems; etc.  308 ) that are inter alia in communication, via a network  304 , with a server  306 . The server  306  comprises inter alia a RDBMS  314 . 
     At a high level clients  302  inter alia submit SQL statements  310  to the RDBMS  314 , an engine  316  of the RDBMS evaluates and processes the SQL statements  310 , and the RDBMS  314  dispatches query results  312  to the clients  308 . 
     The exemplary RDBMS engine  316  that is illustrated in  FIG. 3  comprises: 
     1) A parser  318  that accepts a SQL statement  310  (e.g., as received from a client  302 ), processes (i.e., parses, etc.) the SQL statement  310 , and produces possibly inter alia a query tree. 
     2) A normalized  320  that processes a query tree to inter alia remove redundant operations, complete various error checking and other validation operations, etc. 
     3) A compiler  322  that (a) through an optimizer  324  identifies and evaluates for a query tree a range of query execution plans and then selects a ‘best’ plan and (b) through a code generator  326  generates the code necessary for the RDBMS to realize the selected ‘best’ plan. 
     4) An execution unit  328  that executes inter alia the generated code. 
     5) Various access methods  330  and a database store (page and index manager)  332  that support interactions with inter alia the different tables  334  and indexes  338  that are maintained by the RDBMS  314  to among other things arrive at the information  336  that is required to satisfy (reply to) the SQL statement  310 . 
     The particular components and component arrangement that were depicted in  FIG. 3  are illustrative only and it will be readily apparent to one of ordinary skill in the relevant art that numerous other components and/or component arrangements are easily possible. 
     The present invention may reside within the optimizer component  324  of a RDBMS  314  where it can be used to inter alia enhance substantially the operation, performance, etc. of an optimization algorithm (for simplicity referred to below as ‘algorithm X’) such as for example DPhyp( ), MinCutHyp( ), TopDown( ), etc. (as offered by for example SQL Anywhere from Sybase®) that is executed within a RDBMS optimizer. Such optimization algorithms have several common characteristics including possibly inter alia (1) they exhaustively enumerate valid partitions of the form (S 1 , S 2 ), corresponding to the logical join operation S 1               S 2 , for a subset S=S 1  ∪ S 2  and preserve same in a memoization construct (referred to below as mTable[ ]), (2) generate a plan and then cost the plan for each partition, and (3) then complete various pruning and review operations on the generated/casted plans to inter alia arrive at a ‘best’ plan.
     Aspects of the present invention enhance substantially an algorithm X&#39;s operation, performance, etc. by inter alia ordering the enumerated partitions and generating plans for only a fraction of the partitions, effectively pruning without costing the unpromising partitions. This is accomplished through the preemption of the combined enumeration and costing activity that algorithm X would traditionally complete by (1) saving, uncosted but in an ordered fashion, only some of the enumerated partitions in a memoization construct mTable, (2) generating a plan and then costing the plan for only some subset of the saved partitions, and (3) then selecting a ‘best’ plan. 
       FIG. 4  and reference numeral  400  present, at a high level and in pseudo code, an algorithm ordered-Par( ) that encapsulates aspects of the present invention. The ordered-Par( ) algorithm divides the enumeration and plan generation process of optimization algorithm X into two separate and distinct phases: 
     1) Phase 1, an enumeration phase, preempts the combined enumeration and costing of partitions that algorithm X would traditionally complete by saving, (a) uncosted but (b) in an ordered fashion, only certain of the enumerated partitions for a subset S=S 1  ∪ S 2  in mTable[S] (referred to as Partitions(S)).  FIG. 5  and reference numeral  500  depict, at a high level and in pseudo code, one possible EnumeratePartition( ) algorithm with emphasis directed to two supporting functions—MaxParSize( )  502  and Score( )  504 —that control the operation of this phase. 
     The supporting function MaxParSize(S)  502  identifies or defines, either statically or dynamically, an allowed maximum size for the current subset S. 
     The supporting function Score(S 1 , S 2 )  504  may implement any number of scoring models or paradigms including inter alia: 
     A) MinSel(S 1 , S 2 )=selectivity(p 1              . . .          p n ) where p 1 →p n  are the join predicates which join the subsets S 1  and S 2 .
     B) MinInput(S 1 , S 2 )=cardinality(S 1 )+cardinality(S 2 ). This approach considers the estimated sizes of the input table expressions. 
     C) MinSets(S 1 , S 2 )=∥S 1 ∥−∥S 2 ∥. This approach, which considers the difference between the number of relations of the two children (S 1  and S 2 ), relates the costing of the partitions to how balanced the left and right subtrees are. 
     2) Phase 2, a plan generation phase, where execution plans are generated for only a fraction of the saved partitions based on various constraints so that inter alia unpromising partitions may be dropped (pruned).  FIG. 6  and reference numeral  600  depict, at a high level and in pseudo code, one possible GenerateBestPlan( ) algorithm with emphasis directed to two supporting functions—Score( )  504  (described above) and Budget( )  602 —that direct the operation of this phase. 
     The supporting function Budget( )  602  defines possibly inter alia the desired partition pruning strategy. Among other things the Budget( ) function  602  has, during the execution life of the GenerateBestPlan( ) function, dynamic access to full and complete knowledge of the search space (including inter alia the number of enumerated partitions, the number of partitions that have already been pruned, etc.) and as a result the Budget( ) function  602  can among other things be dynamically adjusted, tuned, redefined, etc. For example, a Budget(S) function might be defined as Budget(S)=CurrentPruneFunction*|Partitions(S| 
     where: 
     A) CostPerPar is the estimated CPU time for costing a partition (as measured μs. 
     B) BestCost(V) is the best estimated cost found this far for a complete plan (as measured in μs). 
     C) TotalPar is the number of partitions that were saved during the enumeration phase. 
     D) CostedPar is the number of partitions that have already been costed. 
     E) PrunedPar is the number of partitions that were pruned without costing. 
     F) CurrentTotalBudget=BestCost(V)/CostPerPar is the current maximum number of partitions to be costed. 
     G) CurrentPruneFunction=(CurrentTotalBudget−CostedPar)/(TotalPar−CostedPar−PrunedPar). 
     The different algorithms that were described above are illustrative only and it will be readily apparent to one of ordinary skill in the relevant art that various enhancements or modifications to an algorithm, numerous alternative algorithms, etc. are easily possible. For example and inter alia: 
     1) Other join enumeration algorithms that possibly inter alia (a) enumerate partitions and (b) employ memoization to save access plans may be substituted for algorithm X. 
     2) Two or more different join enumeration algorithms (that possibly inter alia (a) enumerate partitions and (b) employ memoization to save access plans) may be dynamically selected as an algorithm X during execution of an ordered-Par( ) algorithm. 
     3) In an EnumeratePartition( ) algorithm, sorting and/or pruning may be skipped if for example the search space is determined to be sparse. 
     4) Various enhanced system resource (e.g., memory, etc.) management capabilities may be implemented. As just one example, in the GenerateBestPlan( ) algorithm that is presented in  FIG. 6  the memory that was allocated to a Partitions(S) construct is explicitly released at the end of the routine. 
     5) Any combination of different pruning approaches (e.g., cost-based, etc.) may be employed in a GenerateBestPlan( ) algorithm. 
     6) Any number of different Budget( ) functions may be employed. For example, a Budget(S) function might be defined as Budget(S) ε {min(¼ MaxParSize(S), |Partitions(S)|), 50%|Partitions(S)|100%|Partitions(S)|}. 
     7) A particular join enumeration algorithm (such as inter alia backtracking as offered by for example Sybase&#39;s SQL Anywhere) may be executed first, before an algorithm X is invoked, to obtain inter alia an initial or baseline cost. 
       FIG. 7  through  FIG. 11  present various testing results that were obtained during empirical testing of the ordered-Par( ) algorithm: 
     1)  FIG. 7  and reference numeral  700  capture the results of a particular query being optimized through two different algorithms, DPhyp( ) and ordered-DPhyp( ) (the DPhyp( ) algorithm augmented with the ordered-Par( ) algorithm), where Score( )=MinSel( ), MaxParSize( )=5, and Budget(S)=CurrentPruneFunction*|Partitions(S)|. 
     2)  FIG. 8  and reference numeral  800  capture two particular results (memory consumption and total cost) from a particular query being optimized through two different algorithms, DPhyp( ) and ordered-DPhyp( ) (the DPhyp( ) algorithm augmented with the ordered-Par( ) algorithm), where Score(S 1 , S 2 )=MinSel(S 1 , S 2 ), MaxParSize(S) ε {1, 2, . . . , 20}, and Budget(S) ε {min(¼ MaxParSize(S), |Partitions(S)|), 50%|Partitions(S)|100%|Partitions(S)|}. 
     3)  FIGS. 9 → 11  and reference numerals  900 / 1000 / 1100  capture two particular results (memory consumption and total cost) from a particular query having three different shapes—chain, cycle, and star—being optimized through different algorithms (backtrackingM, DPhyp, MinCutHyp, and TopDown as offered by for example Sybase&#39;s SQL Anywhere) vs. ordered-DPhyp( ) (the DPhyp( ) algorithm augmented with the ordered-Par( ) algorithm), where Score(S 1 , S 2 ) ε {MinSel(S 1 , S 2 ), MinInput(S 1 , S 2 ), MinSets(S 1 , S 2 )}, MaxParSize(S)=10, and Budget(S)=60%|Partitions(S)|. 
     In brief, during testing the ordered-DPhyp( ) algorithm exhibited advantageous characteristics (e.g., the costing of fewer partitions, the efficient consumption of memory, etc.) and yielded lower optimization times. 
     The technology that was described above may be implemented as logical operations and/or modules in or across one or more computer systems. The logical operations may be implemented as a sequence of processor-implemented steps executing in one or more computer systems and as interconnected machine or circuit modules within one or more computer systems. Likewise, the descriptions of various component modules may be provided in terms of operations executed or effected by the modules. The resulting implementation details are a matter of choice, dependent on the performance requirements of the underlying system implementing the described technology. Accordingly, the logical operations making up the embodiments of the technology described above are referred to variously as operations, steps, objects, or modules. Furthermore, it should be understood that logical operations may be performed in any order, unless explicitly claimed otherwise or unless a specific order is inherently necessitated by the claim language. 
     The above specification provides a complete description of the structure and use of exemplary embodiments of the present invention. Although various embodiments of the invention have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, it is to be understood that such material is exemplary only and it is not intended to be exhaustive or to limit the invention to the specific forms disclosed. Those skilled in the art could inter alia make numerous alterations to the disclosed embodiments without departing from the spirit or scope of this invention. Changes in detail or structure may be made without departing from the basic elements of the invention as defined in the appended claims. 
     Although the subject matter has been described in language specific to structural features and/or methodological arts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claimed subject matter. 
     The following list defines acronyms as used in this disclosure: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                 Acrony01 
                 Meaning 
               
               
                   
                   
               
             
             
               
                   
                 BIOS 
                 Basic Input/Output System 
               
               
                   
                 CD-ROM 
                 Compact Disc Read Only Memory 
               
               
                   
                 DBMS 
                 Database Management System 
               
               
                   
                 DRAM 
                 Dynamic Random Access Memory 
               
               
                   
                 EPROM 
                 Erasable Programmable Read-Only Memory 
               
               
                   
                 GUI 
                 Graphical User Interface 
               
               
                   
                 I/O 
                 Input/Output 
               
               
                   
                 LAN 
                 Local Area Network 
               
               
                   
                 MEMS 
                 Microelectromechanical Systems 
               
               
                   
                 OS 
                 Operating System 
               
               
                   
                 PC 
                 Personal Computer 
               
               
                   
                 PCMCIA 
                 Personal Computer Memory Card International 
               
               
                   
                   
                 Association 
               
               
                   
                 PDA 
                 Personal Digital Assistant 
               
               
                   
                 PROM 
                 Programmable Read-Only Memory 
               
               
                   
                 RAM 
                 Random Access Memory 
               
               
                   
                 RDBMS 
                 Relational Database Management System 
               
               
                   
                 RF 
                 Radio Frequency 
               
               
                   
                 SQL 
                 Structured Query Language 
               
               
                   
                 WAN 
                 Wide Area Network 
               
               
                   
                 WWW 
                 World Wide Web