Abstract:
A facility for representing a set of items each potentially having a value for each of a group of attributes is described. The items are represented in a database made up of two or more discrete components. Each component corresponds to a proper subset of group of attributes, and represents for every item of the set the values of its proper subset of attributes. Every component is organized such that data items are represented within it in the same order.

Description:
RELATED APPLICATION(S) 
     This application claims the benefit of U.S. Provisional Patent Application No. 60/873,618, filed on Dec. 6, 2006, which is hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The described technology is directed to the field of query resolution techniques. 
     BACKGROUND 
     A user submits a search query in order to identify, among a set of data items, data items having certain characteristics. For example, it is common for users to query a relational database by submitting a query that specifies values of one or more fields present in the database, and receive in return a query result listing records in the database that contain the specified values in the specified fields. Queries may either be applied directly against the authoritative data source containing information about the set of data items, or against a separate index that is optimized for handling certain kinds of queries. 
     In the case of some sets of data items, the data items have attributes of different types that all may be the subject of a query. For example, in addition to relational fields, some conventional database engines support the storage of geographic locations for data items. In such a case, two separate indices are constructed: a relational index whose structure is tailored to identifying data items based upon their relational field contents, and a geographic index whose structure is tailored to identifying data items based upon their geographic locations—such as an R-tree. A query specifying relational attributes alone is typically processed solely against the relational index, while a query specifying geographic attributes alone is typically processed solely against the geographic index. 
     In conventional database systems, a query that specifies attributes of multiple types, sometimes called a “hybrid query,” is first processed against the index appropriate to each attribute type. In the above example, a hybrid query specifying both relational and geographic attributes would be processed independently against both the relational and geographic indices. Each of the indices produces an intermediate query result, sometimes called a “constituent query result,” identifying all of the data items having the specified attributes of the attribute type represented in the index, irrespective of whether they have the attributes of attribute types not represented in the index. In order to obtain a final query result from the constituent query results, the constituent query results must be joined, or “intersected,” so that the final query result contains only data items present in each of the constituent query results. Joining groups of data items such as those contained in the constituent query results is much more efficient if the data items in each group occur in the same order as in the other groups. Because the different indices used to represent the different types of attributes usually have different structures to more effectively identify data items based upon their different attribute types, however, the constituent query results they produce tend to list items in different orders. Accordingly, in the conventional approach, the constituent query results must all be sorted into a common order before joining. 
     This process is illustrated in  FIG. 1 .  FIG. 1  is a data flow diagram showing a conventional process for processing a hybrid query. First, indices  111 - 113 , each representing different attribute types, are initially built and then maintained to reflect changes in the data source. Second, a query  120  received from the user is applied simultaneously against all of the indices to obtain a constituent query result for each of the indices, here constituent query results  131 - 133 . Third, each constituent query result is normalized, such as by sorting it to obtain a normalized query result, here normalized query results  141 - 143 . Finally, the normalized constituent query results are intersected, such as by joining them, to obtain a final query result  150 . 
     Unfortunately, sorting the constituent query results before joining them is often an expensive operation, consuming significant computing resources. Accordingly, an approach to processing a hybrid query without sorting constituent query results would have significant utility. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a data flow diagram showing a conventional process for processing a hybrid query. 
         FIG. 2  is a high-level data flow diagram showing data flow within a typical arrangement of components used to provide the facility. 
         FIG. 3  is a block diagram showing some of the components typically incorporated in at least some of the computer systems and other devices on which the facility executes. 
         FIG. 4  is a data flow diagram showing a typical process for processing a hybrid query performed by the facility. 
         FIGS. 5A-5C  are table diagrams showing a text index, a geographic index, and a relational index. 
         FIG. 6  is a flow diagram showing steps typically performed by the facility in order to process a hybrid query. 
         FIGS. 7A-7C  show text, geographic, and relational constituent results. 
         FIG. 8  a table diagram showing a final result generated by the facility for the sample query shown in Table 2 by joining the constituent results shown in  FIGS. 7A-7C . 
         FIGS. 9-13  show sample displays presented as part of the user interface. 
         FIGS. 14-16  are flow diagrams showing steps typically performed by the facility in order to present the query specification user interface described above. 
         FIG. 17  is a flow diagram showing steps typically performed by the facility in order to select the items to be displayed in a particular page of a search result. 
     
    
    
     DETAILED DESCRIPTION 
     A software facility for handling search queries (“the facility”) is described. In some embodiments, the facility uses an index, sometimes referred to as a “compound index,” that is specially adapted to resolving hybrid queries that specify two or more different kinds of search criteria to identify data items in a database satisfying the criteria included in the query. 
     For example, in some embodiments, the facility uses a compound index to resolve queries including criteria of any of the following three types: (1) textual criteria that specify textual attributes of a data item; (2) relational criteria that specify relational attributes of a data item; and (3) geographic criteria specifying geographic location attributes of a data item. In some embodiments, the compound index is made up of (1) an inverted index representing the textual attributes of each data item; (2) an indexed relational database made up of one or more tables representing the relational attributes of each data item; and (3) a geopoint table representing the geographic attributes of each data item, where item IDs that identify items in the inverted index correspond to the order of rows representing items in the tables of the relational database as well as the order of rows representing items in the geopoint table. When textual criteria from the query are applied against the inverted index, relational criteria from the query are applied to the relational database, and geographic criteria from the query are applied to the geopoint table, the resulting three constituent result sets can be joined together to form a final result set without having to first sort any of the constituent result sets, as each constituent result set is ordered in accordance with the item IDs. 
     In some embodiments, the facility provides a user interface that permits a user to create a query by specifying values or ranges of values (hereafter “values”) for each of a number of item attributes. Some of these values are always displayed within the user interface, while others are displayed only when a drop-down menu containing them is selected by the user. Whenever a new value is specified for an attribute, the facility (1) processes a query selecting items having the specified values and/or ranges of values to obtain a result set; (2) identifies any attribute whose values are displayed but for which no value has yet been specified; (3) in a single pass through the result set, counts the number of items having each of the displayed attribute values; and (4) displays the count for each of the displayed attribute values next to the attribute value. In the case of some attributes whose values are widely-variable, the facility (5) establishes a large number of “bins” (such as 50 bins) each corresponding to a small range of values of the attribute; (6) as part of (3), for each bin, counts the number of items having a value of the attribute within the range for the bin; and (7) collapses the large number of bins to a smaller number of bins, such a four bins, each containing a roughly similar number of items and generally corresponding to larger ranges than the original bins; and (8) in (4), displays the attribute value ranges and counts for the collapsed bins. This approach provides a powerful query specification user interface while consuming reasonable quantities of computing resources. 
     In some embodiments, the facility uses a paging technique to display the results generated for a search query. Where a user has requested the display of n items per page in a paged search result, each time the user requests the mth page of a search result, the facility (1) reruns the query on which the search result is based; (2) performs a repeatable, or “stable,” sort to populate, but not internally sort, each page up to and including the mth page; and (3) internally sorts and displays the data items populated into the mth page. This overcomes the problem of having to expend extraordinary computing resources to avoid unstable paged result sets, in which items of the search result having the same value of the attribute on which the search result sort is based that span a page boundary may be seen to appear on both of the two pages separated by the page boundary. 
       FIG. 2  is a high-level data flow diagram showing data flow within a typical arrangement of components used to provide the facility. A number of web client computer systems  210  that are under user control generate and send page view requests  231  to a logical web server  200  via a network such as the Internet  220 . These requests typically include page view requests and other requests of various types relating to formulating queries, executing queries, and/or displaying and/or paging query results. Within the web server, these requests may either all be routed to a single web server computer system, or may be loaded-balanced among a number of web server computer systems. The web server typically replies to each with a served page  232 . 
     While various embodiments are described in terms of the environment described above, those skilled in the art will appreciate that the facility may be implemented in a variety of other environments including a single, monolithic computer system, as well as various other combinations of computer systems or similar devices connected in various ways. In various embodiments, a variety of computing systems or other different client devices may be used in place of the web client computer systems, such as mobile phones, personal digital assistants, televisions, cameras, etc. 
       FIG. 3  is a block diagram showing some of the components typically incorporated in at least some of the computer systems and other devices on which the facility executes. These computer systems and devices  300  may include one or more central processing units (“CPUs”)  301  for executing computer programs; a computer memory  302  for storing programs and data while they are being used; a persistent storage device  303 , such as a hard drive for persistently storing programs and data; a computer-readable media drive  304 , such as a CD-ROM drive, for reading programs and data stored on a computer-readable medium; and a network connection  305  for connecting the computer system to other computer systems, such as via the Internet. While computer systems configured as described above are typically used to support the operation of the facility, those skilled in the art will appreciate that the facility may be implemented using devices of various types and configurations, and having various components. 
       FIG. 4  is a data flow diagram showing a typical process for processing a hybrid query performed by the facility. First, as is shown and described further below, the facility builds and maintains each of the indices—here indices  411 - 413  in a normalized form, such as by representing the data items in the same order in each of the indices. Second, the facility applies a query  420  received from the user against all the indices to obtain a constituent query result for each of the indices, here constituent query results  431 - 433 . Because of the manner in which the indices were built and maintained, these constituent query results are already in normalized form, and it is not necessary to incur the extra cost in computing resources of sorting them. Third, the facility intersects the constituent query results to obtain a final query result  450 . 
     Table 1 below shows a sample data item among a set of data items searched by the facility. In this case, the sample data item contains various kinds of information about a home. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 home id: 
                 20 
               
               
                   
                 address: 
                 1539 NW 58th St, Seattle, WA 98107 
               
               
                   
                 location: 
                 47.670820, −122.376557 
               
               
                   
                 make me move: 
                 No 
               
               
                   
                 for sale: 
                 No 
               
               
                   
                 recently sold: 
                 No 
               
               
                   
                 price: 
                 $448,310 
               
               
                   
                 bedrooms: 
                 3 
               
               
                   
                 Bathrooms 
                 1 
               
               
                   
                 size: 
                 1,370 sq. ft. 
               
               
                   
                 lot: 
                 6,453 sq. ft. 
               
               
                   
                 type: 
                 single family 
               
               
                   
                 sale date: 
                 10/10/1999 
               
               
                   
                 description: 
                 Cozy bungalow on quiet street. You&#39;ll love  
               
               
                   
                   
                 how the afternoon sun filters into the back yard. 
               
               
                   
                   
               
             
          
         
       
     
     The home has an identifier of 20, and a street address as shown. The home further has a location identified by the shown latitude and longitude values. The home&#39;s make me move, for sale, and recently sold statuses are all no. The home&#39;s price is shown, as are its number of bedrooms and bathrooms, its floor area and lot size, its type and its sale date. Further, a narrative description is shown for the home. 
       FIGS. 5A-5C  show different indices maintained on a group of home data items including the one described in Table 1.  FIG. 5A  is a table diagram showing a text index  510  used to identify home data items among the set of home data items having particular words in their textual descriptions. The text index is made up of rows including shown rows  521 - 530  each representing the occurrence of a single word in the textual description of a single home, and each divided into the following columns: a term column  511  containing the word, and a home id column  512  containing the home id of a home data item containing the word in its textual description. For example, row  525  indicates that the word “cozy” is contained in the textual description of the home data item having home id 20. It can been seen that the rows of the index for each word (e.g., rows  521 - 522  for the word “cottage,” rows  523 - 528  for the word “cozy,” and rows  529 - 530  for the word “cubbies”) occur in increasing order of home id. 
     While  FIG. 5A  and each of the table diagrams discussed below show a table whose contents and organization are designed to make them more comprehensible by a human reader, those skilled in the art will appreciate that actual data structures used by the facility to store this information may differ from the table shown, in that they, for example, may be organized in a different manner; may contain more or less information than shown; may be compressed and/or encrypted; etc. 
       FIG. 5B  shows a geographic index  540  maintained by the facility on the set of home data items. The geographic index is made up of rows including shown rows  551 - 555 , each corresponding to a different home data item, and each divided into the following columns: a home id column containing the home id for the home data item; a latitude column  542  containing the latitude value for the home; and a longitude column  543  containing a longitude value for the home. For example, it can be seen that row  553  indicates that the home data item having home id 20 has a latitude value of 47.670820 and a longitude value of −122.376557. It can be seen that the rows are ordered in increasing order of the home id column. In some embodiments, the facility maintains this order by adding each new data item to the end of the geographic index with a home id that is larger than the largest existing home id. 
       FIG. 5C  shows a relational index  560  used to identify home data items having particular relational values. The relational index is made up of rows such as shown rows  581 - 585 , each of which corresponds to a different home data item and is divided into the following columns: a home id column  561  containing a home id for the home; a for sale column  562  indicating whether the home presently has a for sale status; a make me move column  563  indicating whether the home presently has a make me move status; a recently sold column  564  that indicates whether the home presently has a recently sold status; a price column  565  indicating a price for the home; a beds column  566  indicating the number of bedrooms in the home; a baths column  567  showing the number of bathrooms in the home; a size column  568  showing a measurement of the floor area of the home; a lot column  569  showing a measurement of the area of the home&#39;s lot; a type column  570  indicating the type of the home; and a sale date column  571  indicating the last date on which the home was sold. For example, it can be seen from row  583  that the home having home id 20 does not presently have the for sale, make me move, or recently sold properties; has a price of $348,310; has 3 bedrooms and 1 bathroom; has a floor area of 1,370 square feet and a lot size of 6,453 square feet; is a single family home; and was last sold on Oct. 10, 1999. It can be seen that the rows are ordered in increasing order of the home id. In some embodiments, the facility achieves this result by synchronizing the rows of the relational index with the rows of the geographic index shown in  FIG. 5B . 
       FIG. 6  is a flow diagram showing steps typically performed by the facility in order to process a hybrid query. In steps  601 , the facility receives the query, which specifies two or more types of criteria. An example query discussed further below is shown in Table 2. 
     
       
         
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 Text criterion: 
                 “cozy” 
               
               
                 Geographic criteria: 
                 latitude between 47.670750 and 47.671150; 
               
               
                   
                 longitude between −122.376575 and −122.376490 
               
               
                 Relational criterion: 
                 Price between $300K and $400K 
               
               
                   
               
             
          
         
       
     
     A user may specify the example query, for example, by typing the word “cozy” in a text field; selecting the price range $300K-$400K from a list of price ranges; and navigating a displayed map to show the region encompassing the specified latitude and longitude ranges. 
     In steps  602 - 604 , the facility loops through each type of criterion specified in the query—in the sample query, the text, geographic, and relational criteria. In step  603 , the facility selects from the index for the current criteria type in accordance with the criteria of that type specified in the query to generate a constituent result. In step  604 , if additional criterion types remain to be processed, then the facility continue in steps  602  to process the next criterion type, also the facility continues in steps  605 . 
     Sample constituent results generated based upon the sample query shown in Table 2 and the indices shown in  FIGS. 5A-5C  are shown in  FIGS. 7A-7C .  FIG. 7A  shows a text constituent result  710 . In some embodiments, the facility generates this constituent result by reading the text index until it first encounters the term “cozy,” and copying this row of the index through the last row containing the term “cozy.” In some embodiments, the facility instead jumps to the first row containing the term “cozy,” using an additional index on the index, not shown. It can be seen that the text constituent result contains rows  721 - 726 , corresponding to all of the rows  523 - 528  contain the word “cozy” in the text index shown in  FIG. 5A . It can be seen that the rows of the text constituent result are ordered in increasing order of home id as a result of having been selected from the text index ordered in the same way. 
       FIG. 7B  shows the geographic constituent result  730 . In some embodiments, the facility generates this constituent result by reading each row of the geographic index to determine whether its latitude and longitude both fall within the range specified by the query. It can be seen that rows  741 - 746  all contain home locations within the latitude and longitude ranges specified by the query. It can further be seen that the rows of the geographic constituent result are ordered in increasing order of home id, as a result of the geographic index shown in  FIG. 5B  being ordered in the same manner. 
       FIG. 7C  shows the relational constituent result  730 . In some embodiments, the facility generates this constituent result by reading each row of the relational index to determine whether its attribute values all satisfy the relational constraints of the query. It can be seen that rows  781 - 785  each correspond to a home having a price in the specified range. Here too, the rows are ordered in increasing order of home id, as a result of the relational index shown in  FIG. 5C  having the same order. 
     In step  605 , the facility joins the constituent results generated in step  603 . In step  606 , the facility returns the results of the join operation performed in step  605  as the final result for the query received in step  601 . After step  606 , the facility continues in step  601  to receive and process the next query. 
     Those skilled in the art will appreciate that the steps shown in  FIG. 6  and in each of the flow diagrams discussed below may be altered in a variety of ways. For example, the order of the steps may be rearranged; substeps may be performed in parallel; shown steps may be omitted, or other steps may be included; etc. 
       FIG. 8  a table diagram showing a final result generated by the facility for the sample query shown in Table 2 by joining the constituent results shown in  FIGS. 7A-7C . It contains rows  801 - 803 , containing the following home ids that are common to each of the three constituent results: 19, 20 and 49. 
     In some embodiments, the facility provides a user interface that permits a user to create a query by specifying values or ranges of values for each of a number of item attributes.  FIGS. 9-13  show sample displays presented as part of the user interface. 
       FIG. 9  is a display diagram showing an initial display of the user interface presented by the facility. The display  900  corresponds to a search query and its result. A map  920  has been generated for inclusion in the display based upon the user having entered the address for a home shown near the center of the map in fields  901  and  902 , then activating button  903 . In response, the facility displayed the map  920  that is shown, centered on the home in question at an intermediate zoom level. The borders of the map have established a geographic criterion for the search. Accordingly, the current search result is a list  950  (only partially shown here) of all the homes that are located within the present borders of the map. The user can navigate to different pages of the query result using controls  904  and  905 . The user may alter the geographic query criterion by navigating the map, such as by scrolling the map in a direction using control  921 , or by changing its zoom level using zoom control  922 . When the user changes the boundaries of the map in this way, the facility updates the geographic query criterion to include the present boundaries of the map, and executes the updated query to generate a new search result that includes the homes within the new boundaries. The user may also specify relational criteria for the search query using panel  910 , which is discussed in greater detail below in connection with  FIGS. 10-13 . Though not shown in  FIG. 9 , in some embodiments, the facility includes in the query specification user interface it presents a mechanism usable by the user to specify a textual criteria for the query, such as a text field. 
       FIG. 10  is a display diagram that shows panel  910 , which is usable by the user to specify relational criteria for the query, in greater detail as panel  1010 . Panel  1010  includes indications  1011 - 1014  of a number of different home statuses. For example, the for sale status  1011  is active for any home that is known to be presently for sale. The checkbox at the left end of the indication indicates that homes having this status are included in the search result. The parenthetical number at the right end of indication  1011  indicates that eight of the homes presently in the search result have this status. Panel  1010  further has a number of subpanels  1020 ,  1030 ,  1040 ,  1050 ,  1060 ,  1070 , and  1080  each corresponding to a different relational attribute, which are each shown here in collapsed form. By selecting the control at the left end of one of these subpanels, the user can expand it in order to specify additional relational criteria. For example, the user may select control  1021  in order to specify a relational criterion for the query that is based upon the price attribute. 
       FIG. 11  is a display diagram showing an expanded version of the price attribute subpanel in the facility when the user selects control  1021 . The expanded price attribute subpanel  1180  lists a number of subranges of the price attribute that may be selected by the user in order to specify a query criterion for the price attribute. A first indication  1181  may be selected by the user to collapse subpanel  1180  without specifying a subrange of the price attribute for inclusion in the query. On the other hand, the user may select any of indications  1182 - 1184  in order to specify a query criterion for the displayed range. For example, the user may select indication  1184  in order to add to the query a criterion requiring a price attribute to be between $300 k and $400 k. The parenthetical at the right end of this indication indicates that, among the homes contained in the current query result, six of them fall into this range and would satisfy such a criterion. The user may also enter a custom range into fields  1185  and  1186 , and select control  1187  in order to create a query criterion for the custom range. 
       FIG. 12  is a display diagram that shows panel  1210  after the user has selected indication  1184  in  FIG. 11 . By comparing  FIG. 12  to  FIG. 10 , it can be observed that the facility has updated the counts displayed for each of statuses  1211 - 1213  shown in the panel to reflect the number of homes having these statuses in the query result for the updated query containing/the price criterion specified by the user in selecting indication  1184 . Additionally, it can be seen that collapsed price subpanel  1220  now contains an indication that this attribute has been constrained to the specified range. The user may go on to specify additional criteria, or select the clear all filters control  1291  to delete the existing relational criterion from the query. 
       FIG. 13  shows a sample display presented by the facility when the user goes on to select control  1251  to expand the collapsed size subpanel  1250 . The expanded subpanel  1350  contains ranges for the size attribute and an indication for each range of the number of homes in the current query result that fall into each subrange. For example, indication  1353  shows that two homes in the current search result have a size attribute value between two thousand and three thousand square feet. Again, the user may make a selection in expanded size panel  1350  to add to the query another relational criterion specifying a particular subrange for the size attribute. 
       FIG. 14  is a flow diagram that shows steps typically performed by the facility in order to present the query specification user interface described above. In step  1401 , the facility receives the specification of an attribute value or range from the user, such as is described above in connection with  FIGS. 9 ,  11 , and  13 . In step  1402 , the facility performs a query that includes any attribute values and ranges specified by the user. In step  1403 , the facility identifies attributes that are or can be displayed for which the user has specified no value or range. In step  1404 , the facility establishes counters for values or ranges of identified attributes. 
       FIG. 15  is a flow diagram showing additional details of step  1404 . In steps  1501 - 1506 , the facility loops through each attribute identified in step  1403 . In step  1502 , if the values for this attribute are enumerated (e.g., yes/no, or condominium/single family), then the facility continues in step  1503 , else (e.g., for price, size, etc., attributes), the facility continues in step  1504 . In step  1503 , the facility establishes a counter for each enumerated value of the attribute. After step  1503 , the facility continues in step  1506 . 
     In step  1504 , the facility divides the range of possible values for the attribute into a large number of subranges, also called “bins.” As one example, the facility may establish 101 subranges for the price attribute: 100 $20,000-wide subranges between zero and $2,000,000, and a subrange over $2,000,000. In step  1505 , the facility establishes a counter for each bin established in step  1504 . In step  1506 , if additional identified attributes remain to be processed, then the facility continues in step  1501  to process the next identified attribute, else the facility returns. 
     Returning to  FIG. 14 , in step  1405 , in a single pass through the query result generated in step  1402 , the facility updates all of the counters established in step  1404 . In step  1406 , the facility consolidates attribute value bins and their counters in order to be able to display a reasonable number of subranges. 
       FIG. 16  is a flow diagram showing details of step  1406 . In steps  1601 - 1604 , the facility loops through each attribute identified in step  1403 . In step  1602 , if the values for this attribute are enumerated, then the facility continues in  1604 , else the facility continues in step  1603 . In step  1603 , the facility consolidates the bins established for the attribute for a smaller number of bins, each containing a similar number of items. For example, from the 101 bins established for the price attribute, the facility may form four consolidated bins, each containing approximately one quartile of the homes counted among all 101 original bins. In step  1604 , if additional identified attributes remain to be processed then the facility continues in step  1601  to process the next identified attribute, else the facility returns. 
     Returning to  FIG. 14 , in step  1407 , the facility displays the values and ranges for the identified attributes and their counters as shown in  FIGS. 12 and 13 . 
     In some embodiments, as shown in  FIG. 9 , the facility uses a paging technique to display the results generated for a search query. Using controls presented as part of the user interface for presenting the search result, the user can request the display of any mth page of n items of the search result. In various embodiments, the number of items n on a page of the search result is preestablished by the designer of the facility, and/or configurable by the user. 
       FIG. 17  is a flow diagram showing steps typically performed by the facility in order to select the items to be displayed in a particular page of a search result. In step  1701 , the facility receives a copy of the query, a page size—that is, the number of items to be shown on each page of the search result, a page number of the search result to be returned, and one or more attributes of the data items on which to sort the data items, and a sort direction that indicates whether the search result will be sorted in increasing or decreasing order of the sort attribute. For example, the request received in step  1701  may specify to return page number two where each page contains five items, and sort in increasing order of a particular attribute. In step  1702 , the facility processes the query to obtain the corresponding search results, such as by using the process described above in connection with  FIGS. 4-8 . A sample search result generated in step  1702  is shown below in Table 3. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 initial order 
               
             
          
           
               
                 position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
             
          
           
               
                 id 
                 12 
                 97 
                 44 
                 68 
                 6 
                 72 
                 41 
                 43 
                 42 
                 22 
                 98 
                 6 
                 33 
                 81 
                 25 
                 24 
                 69 
                 88 
                 11 
                 31 
               
               
                 sort value 
                 2 
                 3 
                 10 
                 18 
                 14 
                 9 
                 3 
                 3 
                 20 
                 17 
                 15 
                 3 
                 19 
                 12 
                 8 
                 16 
                 10 
                 1 
                 13 
                 3 
               
               
                   
               
             
          
         
       
     
     Table 3 shows a search result containing 20 items. The table shows, for each of the 20 positions in the search result, the item ID of the item in that position, as well as the value of the attribute on which the items are being sorted for that item. 
     In steps  1703 - 1705 , the facility loops through each page of the search result from the first page to the page to return. In steps  1704 , the facility populates the current page by sorting the portion of the search result from the beginning of the current page to the end of the search result up to the point at which the current page contains the largest or smallest values in this range as specified by the sort direction. The facility typically uses a repeatable, or “stable,” sort algorithm to avoid the problem of instability. In some embodiments, the facility uses a truncated quicksort algorithm to perform this sorting. In some embodiments, the facility employs a fat pivot as part of the sorting process. In some embodiments, the facility uses a deterministic basis for selecting a pivot as part of the sorting process. In step  1705 , if additional pages remain to be processed, then the facility continues in step  1703  to process the next page, else the facility continues in step  1706 . 
     Table 4 below shows the results of the first iteration of the loop of step  1703 - 1705 . 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 populate first page 
               
             
          
           
               
                 position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 | 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
             
          
           
               
                 id 
                 12 
                 6 
                 43 
                 88 
                 97 
                 | 
                 22 
                 31 
                 81 
                 42 
                 44 
                 68 
                 6 
                 69 
                 33 
                 72 
                 41 
                 11 
                 24 
                 98 
                 25 
               
               
                 sort value 
                 2 
                 3 
                 3 
                 1 
                 3 
                 | 
                 17 
                 3 
                 12 
                 20 
                 10 
                 18 
                 14 
                 10 
                 19 
                 9 
                 3 
                 13 
                 16 
                 15 
                 8 
               
               
                   
               
             
          
         
       
     
     It can be seen by comparing Table 4 to Table 3 that data items 6, 12, 43, 88, and 97—having the lowest sort values 1-3 among the items in the search result—have been sorted into the first page of five items in the search result. It is further noted that (a) the items within the first page are not ordered in accordance with sort value, and (b) the items beyond the first page are also not ordered in accordance with sort value. 
     Table 5 below shows the results of the second iteration of the loop of step  1703 - 1705 . 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 populate second page 
               
             
          
           
               
                 position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 | 
                 6 
                 7 
                 8 
                 9 
                 10 
                 | 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
             
          
           
               
                 id 
                 12 
                 6 
                 43 
                 88 
                 97 
                 | 
                 69 
                 25 
                 41 
                 72 
                 31 
                 | 
                 6 
                 42 
                 81 
                 24 
                 11 
                 68 
                 22 
                 98 
                 44 
                 33 
               
               
                 sort value 
                 2 
                 3 
                 3 
                 1 
                 3 
                 | 
                 10 
                 8 
                 3 
                 9 
                 3 
                 | 
                 14 
                 20 
                 12 
                 16 
                 13 
                 18 
                 17 
                 15 
                 10 
                 19 
               
               
                   
               
             
          
         
       
     
     It can be seen Table 5 to Table 4 that the second iteration of the loop has not affected the data items on the first page of the search results. It can further be seen that data items 25, 31, 41, 69, and 72—having the lowest sort values 3-10 among the items in position 6-20 of the search result—have been sorted into the second page of five items in the search result. It is further noted that (a) the items within the second page are not ordered in accordance with sort value, and (b) the items beyond the second page are also not ordered in accordance with sort value. In the example, after the second iteration of the loop, the loop concludes 
     In step  1706 , the facility sorts the items within the page to return. In some embodiments, the facility uses a sort algorithm such as insertion sort in step  1706 . Table 6 below shows the result of sorting the items within the second page of the sample search result. 
     
       
         
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 sort second page 
               
             
          
           
               
                 position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 | 
                 6 
                 7 
                 8 
                 9 
                 10 
                 | 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
               
               
                   
               
             
          
           
               
                 id 
                 12 
                 6 
                 43 
                 88 
                 97 
                 | 
                 41 
                 31 
                 25 
                 72 
                 69 
                 | 
                 6 
                 42 
                 81 
                 24 
                 11 
                 68 
                 22 
                 98 
                 44 
                 33 
               
               
                 sort value 
                 2 
                 3 
                 3 
                 1 
                 3 
                 | 
                 3 
                 3 
                 8 
                 9 
                 10 
                 | 
                 14 
                 20 
                 12 
                 16 
                 13 
                 18 
                 17 
                 15 
                 10 
                 19 
               
               
                   
               
             
          
         
       
     
     It can be seen by comparing Table 6 to Table 5 that the facility has sorted the data items in the second page in increasing order of their short values. 
     In step  1707 , the facility returns the sorted page. In the example, the facility returns positions 6-10 in the search results shown in Table 6. After step  1707 , these steps conclude. 
     By reviewing Tables 4-6, it can be seen how the facility overcomes the instability problem. If the user later again requests the second page of the same search result, the facility again performs two iterations of the loop. Because of the repeatability of the sort algorithm used in step  1704 , the first iteration of the loop has the same result as before, again committing item 6, 43, and 97 having sort value 3 to the first page rather than item 31 or item 41 which both also have sort value 3. Similarly, the second iteration loop has the same result as before: items 31 and 41, the remaining items with sort value 3, are committed to the second page, as is item 69 having sort value 10 to the exclusion of item 44 having sort value 10. If the user later requests the first page of the same search result, the facility executes the loop once, producing the same result shown above in Table 4, such that the items having sort value 3 included in the first page would be 6, 43, and 97, not 31 or 41 which appeared earlier in the second page. If the user later requests the third page of the same search result, the facility executes the loop three times. In the second iteration of these three, the facility commits item 69 having sort value 10 to the second page, making it unavailable for inclusion in the population of the third page in the third iteration of the loop, and ensuring that item 44 having sort value 10 is populated into the third page. 
     It will be appreciated by those skilled in the art that the above-described facility may be straightforwardly adapted or extended in various ways. For example, the facility may be used to search data items of a variety of types, using queries containing criteria of a variety of types. In processing a query, the facility may use a variety of data resources, including both data sources of various types and indices that are of various types. User interfaces presented by the facility for query specification and search result display may have a wide variety of organizations and appearances. Search results page population and sorting performed by the facility may utilize a wide variety of sorting algorithms and associated techniques. While the foregoing description makes reference to particular embodiments, the scope of the invention is defined solely by the claims that follow and the elements recited therein.