Abstract:
A method for processing queries for a document of elements is provided. The document includes a plurality of subsections where each subsection includes at least a portion of elements in the document. The method comprises: receiving a query for a npath of elements in the document of elements; determining a plurality of step queries from the query, each step query including at least a part of the path of elements; for each step query in the plurality of step queries, determining one or more subsections that include elements that correspond to a step query; and determining at least one subsection that includes the path of elements of the query. A result for the query is generated using the at least one subsection.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/389,066, filed Jun. 13, 2002, entitled “PARENT-CHILD QUERY INDEXING FOR XML DATABASES,” which disclosure is incorporated herein by reference for all purposes. The present disclosure is related to the following commonly assigned co pending U.S. patent applications: Ser. No. 10/462,100, filed on the same date as the present application, entitled “A SUBTREE STRUCTURED XML DATABASE” (hereinafter “Lindblad I-A”); Ser. No. 10/462,023, filed on the same date as the present application, entitled “XML DB TRANSACTIONAL UPDATE SYSTEM” (hereinafter “Lindblad III-A”); and Ser. No. 10/461,935, filed on the same date as the present application, entitled “XML DATABASE MIXED STRUCTURAL-TEXTUAL CLASSIFICATION SYSTEM” (hereinafter “Lindblad IV-A”); 
     The respective disclosures of these applications are incorporated herein by reference for all purposes. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention generally relates to accessing data and more specifically to retrieving elements of documents using step queries generated from a query. 
     Many languages, such as Extensible Markup Language (XML), define rules that are used for structuring data. An XML document is created using the rules to structure data and includes two parts: the marked up document and the document schema. The marked up part of the document encodes a description of the document&#39;s storage layout and logical structure. The schema part specifies constraints that define XML document structures. 
     XML documents are made up of storage units called elements, which may be nested to form a hierarchical structure. An element may contain either parsed or unparsed data. Parsed data is made up of characters, some of which form character data, and some of which form the markup; unparsed data is data in its native format. Also, XML elements may have associated attributes, which may be referred to as name-value pairs. Elements and attributes are described in XML schema where the schema includes, for each element that may occur in the document, a name, the type, the set of attributes, and the set of allowable constituent elements. The relations are represented in a graph with one vertex for each element name, and one edge from an element to each possible constituent. 
     In managing XML documents, retrieving elements in the documents for reading or reformatting is often necessary. Accordingly, several query languages have been proposed for searching for and retrieving elements in the XML documents. For example, XQuery, a language derived from an XML query language Quilt and borrowing features from other languages, including XPath, is used for accessing elements in an XML document. XQuery accesses an element using a feature from XPath called an XPath location path expression, which specifies a pattern of elements within the XML document. For example, a query may be of the form A/B/C/D, and is interpreted to specify a pattern of the elements A, B, C, and D within the structure of the XML document. In order to find the desired element D, a system traces the hierarchy of the XML document. The system finds in order, all instances of the element A, all instances of the element B related to element A, all instances of the element C related to the A/B group, and all instances of the element D related to the A/B/C group. Thus, the system processes the XQuery command sequentially, starting from the first element and then to each subsequent element. This method of accessing elements in an XML document becomes time consuming and requires extensive computing power, especially when an element is deeply nested in a hierarchical XML document or a query includes a long path of elements. 
     BRIEF SUMMARY OF THE INVENTION 
     In one embodiment of the present invention, a method for processing queries for a document of elements is provided. The document includes a plurality of subsections where each subsection includes at least a portion of elements in the document. The method comprises: receiving a query for a path of elements in the document of elements; determining a plurality of step queries from the query, each step query including at least a part of the path of elements; for each step query in the plurality of step queries, determining one or more subsections that include elements that correspond to a step query; and determining at least one subsection that includes the path of elements of the query. In one embodiment, a result for the query is generated using the at least one subsection. 
     A further understanding of the nature and advantages of the invention herein may be realized by reference of the remaining portions in the specifications and the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of a simple XML document including text and markup. 
         FIG. 2  is a schematic representation of the XML document shown in  FIG. 1 ;  FIG. 2A  illustrates a complete representation the XML document and  FIG. 2B  illustrates a subtree of the XML document. 
         FIG. 3  is a schematic representation of a more concise XML document. 
         FIG. 4  illustrates a portion of an XML document that includes tags with attributes;  FIG. 4A  shows the portion in XML format;  FIG. 4B  is a schematic representation of that portion in graphical form. 
         FIG. 5  shows a more complex example of an XML document, having attributes and varying levels. 
         FIG. 6  is a schematic representation of the XML document shown in  FIG. 5 , omitting data nodes. 
         FIG. 7  illustrates a possible decomposition of the XML document illustrated in  FIGS. 5–6 . 
         FIG. 8  illustrates the decomposition of  FIG. 7  with the addition of link nodes. 
         FIG. 9  illustrates an XQuery server (XQE) according to one embodiment; 
         FIG. 10  illustrates a flow chart for a process for generating database according to one embodiment; and 
         FIG. 11  is a flow chart of a process for generating a result for query according to one embodiment. 
         FIG. 12  depicts a PostingList that may be stored using the structure shown in  FIG. 10  according to one embodiment of the present invention. 
         FIG. 13  depicts a PostingList with corresponding scores for each subtree ID according to one embodiment of the present invention. 
         FIGS. 14A–14E  depict PostingList structures for each subtree according to one embodiment of the present invention. 
         FIG. 15A  shows a false positive match and  FIG. 15B  shows a positive match. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     This detailed description illustrates some embodiments of the invention and variations thereof, but should not be taken as a limitation on the scope of the invention. In this description, structured documents are described, along with their processing, storage and use, with XML being the primary example. However, it should be understood that the invention might find applicability in systems other than XML systems, whether they are later-developed evolutions of XML or entirely different approaches to structuring data. 
     Subtree Storage 
     Subtree storage is described in this section, with following sections describing apparatus, methods, structures and the like that might use and store subtrees. Subtree storage is explained with reference to a simple example, but it should be understood that such techniques are equally applicable to more complex examples. 
       FIG. 1  illustrates an XML document  30 , including text and markup.  FIG. 2A  illustrates a schematic representation  32  of XML document  30 , wherein schematic representation  12  is a shown as a tree (a connected acyclic simple directed graph) with each node of the tree representing an element of the XML document or an element&#39;s content, attribute, the value, etc. 
     In a convention used for the figures of the present application, directed edges are oriented from an initial node that is higher on the page than the edge&#39;s terminal node, unless otherwise indicated. Nodes are represented by their labels, often with their delimiters. Thus, the root node in  FIG. 2A  is a “citation” node represented by the label delimited with “&lt; &gt;”. Data nodes are represented by rectangles. In many cases, the data node will be a text string, but other data node types are possible. In many XML files, it is possible to have a tag with no data (e.g., where a sequence such as “&lt;tag&gt;&lt;/tag&gt;” exists in the XML file). In such cases, the XML file can be represented as shown in  FIG. 2A  but with some nodes representing tags being leaf nodes in the tree. The present invention is not limited by such variations, so to focus explanations, the examples here assume that each “tag” node is a parent node to a data node (illustrated by a rectangle) and a tag that does not surround any data is illustrated as a tag node with an out edge leading to an empty rectangle. Alternatively, the trees could just have leaf nodes that are tag nodes, for tags that do not have any data. 
     As used herein, “subtree” refers to a set of nodes with a property that one of the nodes is a root node and all of the other nodes of the set can be reached by following edges in the orientation direction from the root node through zero or more non-root nodes to reach that other node. A subtree might contain one or more overlapping nodes that are also members of other “inner” or “lower” subtrees; nodes beyond a subtree&#39;s overlapping nodes are not generally considered to be part of that subtree. The tree of  FIG. 2A  could be a subtree, but the subtree of  FIG. 2B  is more illustrative in that it is a proper subset of the tree illustrated in  FIG. 2A . 
     To simplify the following description and figures, single letter labels will be used, as in  FIG. 3 . Note that even with the shorted tags, tree  35  in  FIG. 3  represents a document that has essentially the same structure as the document represented by the tree of  FIG. 2A . 
     Some nodes may contain one or more attributes, which can be expressed as (key, value) pairs associated with nodes. In graph theory terms, the directed edges come in two flavors, one for a parent-child relationship between two tags or between a tag and its data node, and one for linking a tag with an attribute node representing an attribute of that tag. The latter is referred to herein as an “attribute edge”. Thus, adding an attribute (name, value) pair to an XML file would map to adding an attribute edge and an attribute node, followed by an attribute value node to a tree representing that XML file. A tag node can have more than one attribute edge (or zero attribute edges). Attribute nodes have exactly one descendant node, a value node, which is a leaf node and a data node, the value of which is the value from the attribute pair. 
     In the tree diagrams used herein, attribute edges sometimes are distinguished from other edges in that the attribute name is indicated with a preceding “@”. FIG. 4A illustrates a portion of XML markup wherein a tag b has an attribute name of “K” and a value of “V”.  FIG. 4B  illustrates a portion of a tree that is used to represent the XML markup shown in  FIG. 4A , including an attribute edge  36 , an attribute node  37  and a value node  38 . In some instances, tag nodes and attribute nodes are treated the same, such as indexing sequences and the like, but other times are treated differently. To easily distinguish tag nodes and attribute nodes in the illustrated trees, tag nodes are delimited with surrounding angle brackets (“&lt; &gt;”), while attribute nodes are be limited with an initial “@”. 
       FIG. 5  et seq. illustrate a more complex example, with multiple levels of tags, some having attributes.  FIG. 5  shows a multi-level XML document  40 . As is explained later below,  FIG. 5  also includes indications  42  of where multi-level XML document  40  might be decomposed into smaller portions.  FIG. 6  illustrates a tree  50  that schematically represents multi-level XML document  40  (with a data nodes omitted). 
       FIG. 7  shows one decomposition of tree  50  with subtree borders  52  that correspond to indications  42 . Each subtree border  52  defines a subtree; each subtree has a subtree root node and zero or more descendant nodes and some of the descendant nodes might in turn be subtree root nodes for lower subtrees. In this example, the decomposition points are entirely determined by tag labels (e.g., each tag with a label “c” becomes a root node for a separate subtree, with the original tree root node being the root node of a subtree extending down to the first instances of tags having tag labels “c”). In other examples, decomposition might be done using a different set of rules. For example, the decomposition rules might be to break at either a “c” tag or an “f” tag, break at a “d” tag when preceded by an “r” tag, etc. Decomposition rules need not be specific to tag names, but can specify breaks upon occurrence of other conditions, such as reaching a certain size of subtree or subtree content. Some decomposition rules might be parameterized where parameters are supplied by users and/or administrators (e.g., “break whenever a tag is encountered that matches a label the user specifies”, or more generally, when a user-specified regular expression or other condition occurs). 
     Note from  FIG. 7  that subtrees overlap. In a subtree decomposition process, such as one prior to storing subtrees in a database or processing subtrees, it is often useful to have nonoverlapping subtree borders. Assume that two subtrees overlap as they both include a common node. The subtree that contains the common node and parent(s) of the common node is referred to herein as the upper overlapping subtree, while the subtree that contains the common node and child(ren) of the common node is referred to herein as the lower overlapping subtree. 
       FIG. 8  illustrates one approach to having nonoverlapping subtrees, namely by introducing the construct of link nodes  60 . For each common node, an upper link node is added to the upper subtree and a lower link node is added to the lower subtree. These link nodes are shown in the figures by squares. The upper link node contains a pointer to the lower link node, which in turn contains a pointer to the root node of the lower overlapping subtree (which was the common node), while the lower link node contains a pointer to the upper link node, which in turn contains a pointer to the parent node of what was the common node. Each link node might also hold a copy of the other link node&#39;s label possibly along with other information. Thus, the upper link node may hold a copy of the lower subtree&#39;s root node label and the lower link node may hold a copy of the upper subtree&#39;s node label for the parent of what was the common node. 
     An XQuery may include an XPath location that indicates a path expression of elements. XPath location path expressions have the form “name_a/name_b/.../name_z”, and specify a pattern of elements within the XML document hierarchical element structure. The terms name_a, name_b, . . . refer to elements or attributes of the XML document. The XPath location path expression is used to specify a desired element that is to be retrieved. For example, if all authors&#39; last names appearing within a “citation” fragment are desired, an XPath location path pattern is A/C/E or citation/author/last. For discussion purposes, the queries processed will be XQuery and XPath queries for XML documents; however, it will be understood that a person skilled in the art will appreciate other queries that may be processed for other documents. Thus, embodiments of the present invention are not limited to XML documents and XQueries. 
       FIG. 9  illustrates an XQuery server (XQE)  200  according to one embodiment. XQE  200  includes a document processor  204  and a query processor  218 . Document processor  204  generates step queries and step query results from documents  202  and stores the step queries and step query results in a database  212 . In one embodiment, documents  202  are parsed documents. For example, parsed documents are created by an XML parsing process. The parsing process accepts XML textual inputs (serialized XML), analyzes the element structure of these documents, and outputs a data structure that represents the input document as a linked collection of element nodes linked to attribute nodes and child element nodes. The parsed XML document also may contain text nodes, processing instruction nodes, and comment nodes. 
     Overview 
     Query processor  218  receives a query  219  for elements in documents  202  and generates step queries from a query  219 . In one embodiment, query  219  is a parsed query. Parsed queries are created by an XQuery parsing process. The XQuery parsing-process accepts XQuery textual inputs, analyzes their grammatical structure, and outputs a data structure that represents the Xquery query as a linked collection of expression nodes. For example, each query expression of the form ‘A op B’ is represented as an op-node with two children nodes representing the subexpressions A and B. The results from the step queries are retrieved from database  212  and a result for query  219  is determined. For example, an intersection of the results is taken to generate the result for query  219 . 
     Document Processing 
     XQE  200  receives documents  202 , such as the XML document of  FIG. 1 . Documents  202  are passed to a document processor  204 , which includes a step query generator  206 , a canonicalizer  208 , a hash key generator  210 , and a step query result generator  214 . After receiving documents  202 , step query generator  206  generates step queries from documents  202 . The step queries are patterns from the hierarchical structure of elements in documents  202 . For example, the step queries are relationships between elements that may be part of possible queries for elements in document  202 . The number of steps, K, in a query represents a number of levels of relationships between elements. A query may be for any number of K steps. A larger K means faster execution but more space is required to store the larger step queries. A smaller K means slower execution but less space is required. For example, a two-step query may be a query for a parent node and its child node and a three-step query may be a query for a parent, its child, and the child&#39;s child. In one embodiment, one-step, two-step, three-step, and four-step queries may be generated from elements in documents  202 . These step queries may take the form of these patterns for: 
     one-step queries:
         (a) elem,   (b) word::wrd;
 
two-step queries:
   (c) elem/word::wrd,   (d) elem/word::[string],   (e) elem/child,   (f) elem/@attr;
 
three-step queries:
   (g) elem/attr/word::wrd,   (h) elem/@attr/word::[string],   (i) elem/child/word::wrd,   (j) elem/child/word::[string],   (k) parent/elem/child;
 
and four-step queries:
   (l) elem/child/@attr/word::wrd,   (m) elem/child/@attr/word::[string],   (n) parent/elem/child/word::wrd,   (o) parent/elem/child/word::[string],   (p) grandp/parent/elem/child.       

     It will be understood that step queries are not limited to the above queries and other step queries may be used and derived from documents  202 . 
     Once the step queries are generated from documents  202 , the step queries are passed to canonicalizer  208 . Canonicalizer  208  reduces each step query to its canonical form. For example, the one-step queries are reduced to the following canonical forms: 
                                                 (a) elem   −&gt; elem,           (b) word::wrd   −&gt; wrd;                        
the two-step queries to the following canonical forms:
 
                                                 (c) elem/word::wrd   −&gt; elem#word(“wrd”),           (d) elem/word::[string]   −&gt; elem#string,           (e) elem/child   −&gt; elem/#child,           (f) elem/@attr   −&gt; elem#/@#attr;                        
the three-step queries to the following canonical forms:
 
                                                 (g) elem/@attr/word::wrd   −&gt; elem#/@#attr#word(“wrd”),           (h) elem/@attr/word::[string]   −&gt; elem#/@#attr#string,           (i) elem/child/word::wrd   −&gt; elem#/#child#word(“wrd”),           (j) elem/child/word::[string]   −&gt; elem#/#child#string,           (k) parent/elem/child   −&gt; parent#/#elem#/#child;                        
and the four-step queries to the following canonical forms:
 
     
       
         
               
               
             
           
               
                   
               
             
             
               
                 (l) elem/child/@attr/word::wrd 
                 −&gt; elem#/#child/@#attr#word 
               
               
                   
                 (“wrd”), 
               
               
                 (m) elem/child/@attr/word::[string] 
                 −&gt; elem#/#child/@#attr#string, 
               
               
                 (n) parent/elem/child/word::wrd 
                 −&gt; parent#/#elem#/#child#word 
               
               
                   
                 (“wrd”), 
               
               
                 (o) parent/elem/child/word::[string] 
                 −&gt; parent#/elem#/#child#string, 
               
               
                 (p) grandp/parent/elem/child 
                 −&gt; grandp#/parent#/#elem#/#child; 
               
               
                   
               
             
          
         
       
     
     Once the step queries are reduced to their canonical form, the step queries are passed to hash key generator  210 . 
     Hash key generator  210  generates hash keys for each canonical form that may be used for indexing results for each step query. Although hash keys are described, it should be understood that any reference to a storage location may be used. In one embodiment, a 64-bit hash value is computed for each canonical form. Individual names such as parent, element, and child, as well as the literals word (“ ”), /@, and / generate hash values by direct application of a 64-bit hashing function in hash key generator  210 . Also, terms (tokens) separated by the hash mark “#” may be composed by applying either the formula A#B=hash64(A)*5+hash64(B), or the formula A#B=hash64(hash64(A), B), where hash64 represents the hashing function. The latter formula expresses a general compositional mechanism for forming the hash key for two tokens using previously computed hash values for the first token. Hash key generator  210  uses hash value caches and hash composition to compute hash keys for all the indexable step queries. 
     For example, the hash key for elem#/@attr is computed by the hashing function as:
 
hash64(elem)*5+(hash64(/@)+hash64(attr));
 
and the hash key for A#B#C is computed as:
 
hash64(hash64(hash64(A),B),C)
 
and the hash key for A#B#C# . . . #Y#Z is computed as
 
hash64(hash64( . . . (hash64(hash64(hash64(A),B),C), . . . , Y),Z).
 
     Additionally, the hash key for a string value, such as: string=word — 1 word — 2 . . . word_n, is computed by composition across the word tokens within the string. Thus, the hash key is computed as follows:
 
( . . . (hash64(word — 1)*5+hash64(word — 2)*5+ . . . )*5+hash64(word_n)).
 
     The hash keys generated from hash key generator  210  are stored in an index  213  of database  212 . Also, the hash keys for each canonical step query are used to access step query results stored in index  213  of database  212 . The step query results are generated by step query result generator  214 . Step query result generator  214  receives the step queries generated from step query generator  206  and generates the results for each step query using the hierarchical structure of documents  202  corresponding to the step query. In one embodiment, the step query results may be the element(s) corresponding to the step query. In another embodiment, the step query results for a step query are one or more sub-tree IDs corresponding to the XML fragment for the step query. The step query and corresponding step query results may be stored as a PostingList, which will be described below. Additionally, a frequency count of how many times the step query result occurs within the XML fragment is connected with the step query result. Once the results for the step queries are determined, step query result generator  214  stores the results in index  213 . In one embodiment, index  213  includes, but is not limited to, the results of all atomic one-step queries of the forms:
         (a) find all elements with a given name,   (b) find all elements containing a given word;
 
in addition, it includes the results of all two-step queries of the forms:
   (c) find all elements of a given name whose text content contains a given word,   (d) find all elements of a given name whose text content equals a given string,   (e) find all elements of a given name with a child element of a given name,   (f) find all elements of a given name with an attribute of a given name;
 
in addition, it includes the results of all three-step queries of the forms:
   (g) find all elements of a given name with an attribute of a given name whose value contains a given word,   (h) find all elements of a given name with an attribute of a given name whose value equals a given string,   (i) find all elements of a given name with a child element of a given name whose text content contains a given word,   (j) find all elements of a given name with a child element of a given name whose text content equals a given string,   (k) find all elements of a given name with a parent of a given name and a child element of a given name;
 
and in addition, it includes the results of all three-step queries of the forms:
   (l) find all elements of a given name with a child element of a given name with an attribute of a given name whose value contains a given word,   (m) find all elements of a given name with a child element of given name with an attribute of a given name whose value equals a given string,   (n) find all elements of a given name with a parent element of a given name with a child element of a given name whose text content contains a given word,   (o) find all elements of a given name with a parent element of a given name with an element of a given name with a child element of a given name whose text content equals a given string,   (p) find all elements of a given name with a grandparent element of a given name with a parent element of a given name with an element of a given name and a child element of a given name;       

     It will be understood that the step query results are not limited to the above possibilities and may store atomic query results up to any fixed finite level. 
     In one embodiment, index  213  is an inverted file index. The inverted file index maps terms to PostingLists. The terms correspond to textual units extracted from a collection of documents  202  or document fragments from documents  202 , and PostingLists describe where and how often each term appeared within a given document or document fragment from documents  202 . In one embodiment, ‘terms’ are the atomic text units of document  202 . Terms are generated by ‘tokenizing’ the text content of the document. Text is tokenized through a process of table lookup for each character to determine if that character is a word constituent, white space, or punctuation. Word constituent characters delimited by either spaces or punctuation are accumulated as ‘tokens’. Canonicalized step queries are also terms. 
     In one embodiment, a hash key is stored in a memory-map list index file in index  213  whose entries contain (key, offset) pairs, where the offset describes the absolute location within a Listdata file where the list of results for the step query may be found. Thus, the Listdata file includes a reference to the step query results. In one embodiment, the step query results are stored as a compressed list of (subtree-id, frequency-count) pairs. A subtree-id uniquely identifies the XML fragment matching the atomic step query, and the frequency-count describes the approximate number of times that the match occurred within document  202  or the document fragment of document  202 . 
     In one embodiment, a list of results in the ListData file may be referred to as the PostingList. The PostingList includes the unique subtree-id identifier of the corresponding result of the step query. Additionally, the PostingList includes a score, which is a normalized frequency count. For example, index  213  stores, for each term, at a location determined by the hash key of that term, a PostingList containing references to the subtrees containing the term along with a normalized frequency count (score) that approximates the number of occurrences of the term within the subtree. In one embodiment, the sequence of nodes returned by the function search may be ordered by a ‘relevance’ score. The relevance of a node to the specified query is a complex function that depends on the frequency the query terms appear in the text of the query nodes, the frequency the query terms appear across the entire database, and the quality score attached to a given node. The quality score is further described in Linblad IV-A. In one embodiment, the PostingLists are stored in a compressed format. Although the PostingList is described, it will be understood that other lists may be used to store step query results. 
     Each hash value provides an index into a memory-mapped ListIndex file of fixed-length records. Each record contains a pair including a hash key and a fixed-width file offset. The file offset describes the location within a secondary ListData heap file where the PostingLists are stored. Binary search finds the (key, offset) pair within the ListIndex file, then a single random access I/O to the ListData file locates the first block of PostingList data. In most cases one data block contains the entire PostingList. But if not, and the PostingList exceeds the size of one data block, then subsequent sequential I/O&#39;s fetch the remainder of the list. The number of I/O is proportional the length of the PostingList divided by the packing factor—that is, the number of individual postings per block. 
     In one embodiment, the format uses unary-log-log variable length bit encodings for subtree id&#39;s and scores. Furthermore, both subtree id&#39;s and scores may be kept in a differential form where each Posting stores only the encoded difference from the preceding subtree id and score. Large PostingLists typically have long strings of consecutive subtree id&#39;s with scores that are mostly equal. The PostingList formats encode the consecutive runs using only one or two bits for the delta(id) (the id differential), and delta (score) (the score differential). Large PostingLists are stored with markers containing sufficient information to allow a search process to skip forward across blocks of Postings (a “skip-list” structure). The skip-list block size a configurable parameter. 
     For any choice of the skip-list block size parameter, three cases may arise: (1) the PostingList size is less than fifteen, (2) the PostingList size is less than or equal to one block, and (3) the PostingList size exceeds a single block. In the following description, the square brackets [ ] indicate ‘unary-log-log variable length bit encoding’. The parentheses indicate bit fields of a specified size, (e.g., length(0:3) means a 4-bit field). The notations {0} and {1} indicate constant bits equal to 0 and 1, respectively. 
     In case (1) the length, being less than 15, occupies four leading bits, and the rest of the format is packed with variable-length bit encodings of differential subtree id&#39;s and scores:
         length(0:3), [id0], [score0],
           [id1−id0], [score1−score0],   [id2−id1], [score2−score1],   [id3−id2], [score3−score2], . . .   
               

     In case (2), the four leading bits are all set to 0, and the format is:
         {0}(0:3), [length],
           [id0], [score0],   [id1−id0], [score1−score0],   [id2−id1], [score2−score1],   [id3−id2], [score3−score2], . . .   
               

     And in case (3), the four leading bits are all set to 1 and the format is:
         {1}(0:3), [length], Block0, Block1, Block2, . . .
 
Each Block has the format:
   maxSubtreeID[0:32], numPostings[0:15], numWords[0:15]
           [id0], [score0],   [id1−id0], [score1−score0],   [id2−id1], [score2−score1],   [id3−id2], [score3−score2], . . .   
               

     MaxSubtreeID bounds the ordinal size of any subtree id appearing in the block; numPostings bounds the number of Postings in the block and numWords is the size of the block in 32-bit words. 
     A search for a given subtree id proceeds by scanning down the list: if maxSubtreeID is smaller than the given id, then the process skips forward to the start of the next block by incrementing the list offset by numWords. 
     The granularity of index  213  will now be described. More details relating to index  213  and storage of subtree IDs are disclosed in Linblad I-A. Index  213  stores the SubTree ids. The result of searching database  212  with step queries is a list of SubTrees satisfying the step queries. The system synthesizes per-element search query results by loading whole SubTrees into memory of XQE  200  and then seeking within the SubTree for specific elements, attributes, text content, or any of the combinations of elements, attributes and content described above. The SubTree represents a unit of locality. The indexes are designed to speed up queries that can be resolved by locating a contiguous fragment of the original XML document and then navigating within that fragment. 
     In one example, referring to  FIGS. 1 and 2 , document processor  204  may receive the document fragment of  FIG. 1  and generate step queries of the form: 
     one step queries: 
     
         
         
           
             A, B, C, D, E, F; and 
             term — 1, term — 2, term — 3, . . . for each term appearing in A, B, C, . . . ;
 
two-step queries:
 
             A/B, A/C, A/D, C/E, and C/F, and 
             A/word(term — 1), A/word(term — 2), A/word(term — 3), . . . ,
 
three-step queries:
 
             A/C/E, and A/C/F. 
           
         
       
    
     Each of the above step queries may be assigned a hash value and stored in index  213 . The results of the step queries are then computed and stored in step query database  216 . The hash value may then be used to look up the step query results, which point to one or more sub-tree IDs for the XML fragment corresponding to the step query. For example, the step query A/B includes the sub-tree ID for the citation/title fragment. 
     Query Processing 
     One embodiment of query processor  218 , which includes an optimizer  220 , a step query generator  222 , a composer  224 , and an intersector  226 , will now be described. Query processor  218  receives query  219 , generates step queries from query  219 , uses the generated step queries to retrieve the pre-computed step query results in database  212 , and uses the step queries to output a query result. Thus, when a query is received for documents  202 , the results for step queries generated from the query are already known. 
     After receiving query  219 , query processor  218  sends query  219  to optimizer  220 , which may optimize the query if necessary. The optimization process will be described in more detail below. The optimized query is then sent to a step query generator  222 . 
     Step query generator  222  generates step queries from query  219 . As described above, with reference to step query generator  206 , step query generator  222  breaks query  219  into step queries, such as one-step queries, two-step queries, three-step queries, and four-step queries. For example, step query generator  222  reduces or decomposes query  219  of a form:
         aa — 1/aa — 2/aa — 3/aa — 4/.../aa_(n−1)/aa_n (where the ellipses indicate that any finite number of additional steps may appear in the query)
 
to a sequence of two-step queries as follows:
   aa — 1/aa — 2, aa — 2/aa — 3, aa — 3/aa — 4, . . . , aa_(n−2)/aa_(n−1), aa_(n−1)/aa_n.       

     Queries containing trailing attribute specifications, as in aa — 1/aa — 2/aa — 3/aa — 4/.../@aa_n, are reduced to a sequence of two-step queries as follows:
     aa — 1/aa — 2, aa — 2/aa — 3, aa — 3/aa — 4, . . . , aa_(n−2)/aa_(n−1), aa_(n−1)@aa_n.   

     Queries containing trailing word specifications, as in aa — 1/aa — 2/aa — 3/.../aa_n/word::wrd, are reduced to a sequence of two-step queries as follows:
     aa — 1/aa — 2, aa — 2/aa — 3, . . . , aa_(n−1)/aa_n, aa_n/word::wrd.   

     Queries containing trailing attribute word specifications, as in aa — 1/aa — 2/aa — 3/.../aa_(n−1)/@aa_n/word::wrd, are reduced to a sequence of two-step and three-step queries as follows:
     aa — 1/aa — 2, aa — 2/aa — 3, . . . , aa_(n—2)/aa_(n−1), aa_(n−1)/@aa_n/word::wrd.   

     The generated step queries are passed to composer  224 , which accesses database  212  to retrieve the results for the step queries. In one embodiment, composer  224  may reduce the step queries to their canonical form and generate a hash key for the step query with methods as described above. Composer  224  references the hash key values in index  213  to retrieve the results from index  213 . In one embodiment, the results may be one or more subtree IDs for the elements. In another embodiment, the results may be the elements corresponding to the step queries or all of the elements in each subtree. 
     Intersector  226  determines a result for the query using the step query results. The result is one or more subtrees that include all of the step queries. In one embodiment, one or more subtree IDs are returned. In one example, intersector  226  takes the intersection of the results of the step queries to produce a result that includes a result for query  219 . An intersection of the results of the step queries may include some additional unwanted results. A post-processing step may be performed by intersector  226  in which the unwanted results are eliminated. For example, the post-processing step matches each step query element of the intersection against the original query. After post-processing, the query result is outputted. 
     The optimization process implemented by optimizer  220  will now be described. Optimizer  220  may optimize query  119  by rewriting query  119  in a form that may be used by step query generator  222  to generate optimized step queries. For example, optimizer  220  includes rewriting rules where queries  119  are rewritten in terms of the pre-computed step queries. 
     For example, optimizer  220  may rewrite path expressions of the form aa — 1//aa — 2 by consulting a tree structure that represents the set of relations among the elements described for document  202  for which the query is intended. The ‘//’ operator specifies the set of all nodes appearing below a given element node in the document tree. For example, ‘A//B’ specifies the set of all the element nodes labeled ‘B’ which are strict descendants of ‘A’. In one embodiment, optimizer  220  references elements described in XML schema where the schema includes, for each element that may occur in the document, a name, the type, the set of attributes, and the set of allowable constituent elements. The relations are represented in a graph, such as the one shown in  FIG. 1 , with one vertex for each element name, and one edge from an element to each possible constituent. 
     Given an XPath location path expression of the form aa — 1//aa — 2, optimizer  220  attempts to determine a set of all possible sequences that interpolate the “//” (descendent-or-self::) step. The ‘descendant-or-self::’ operator specifies the set of all nodes at or below a given node in the document tree. For example, ‘A/descendant-or-self::B’ specifies the set of all descendants, including ‘A’, of the element node ‘A’. For example, referring to  FIG. 2 , the expression A//E may be written as (A/B/E union A/C/E). In some cases, the XPath location expression A//E may have an unlimited number of legal expansions. In this case, optimizer  220  does not attempt to rewrite the expression. 
     The optimized query is then passed to step query generator  222  for processing into step queries. The results to the step queries are retrieved as described above and the intersection taken by intersector  226 . In post-processing, contiguous portions (maximal sequences of “/” separated steps) are processed as described above. Then, the results for the contiguous portions are then post-processed to verify the descendent relation by following parent links for the residual “//” steps. For example, the location path expression A/C//B/E will be optimized as the pair of index queries A/C, B/E and for each node returned by the B/E parent links followed, parent links are followed to verify that some ancestor appears in the node set returned by A/C. The post-processing is done by creating an auxiliary hash index for the node ids occurring in A/C. 
     The post-processing step takes a sequence of subtree ids returned by the query composer and intersector, and scans these subtrees for the purpose of resolving general XPath location path expressions. A general XPath location path has the following syntax:
 
A[p — 11]...[p — 1a]/B[p — 21]...[p — 2b]/C[p — 31]...[p — 3c]/.../T[p_k1]...[pkt]
 
or
 
A[p — 11]...[p — 1a]/B[p — 21]...[p — 2b]/C[p — 31]...[p — 3c]/.../@T[p_k1]...[pkt]
 
     Each of A, B, C, . . . , T is an element label, and the last step T may be either an element label, an attribute label, or a non-element node type selector, e.g., ‘text( )’ for text nodes, ‘comment( )’ for comment nodes, and ‘pi( )’ for processing instruction nodes. Each p_ij is a predicate expression that may involve as inputs additional (nested) XPath expressions, or in the case of XQuery, variables from an enclosing scope. The post-processing step starts with a set of nodes corresponding to the last step. These are extracted from the subtrees appearing in the intersection of the pair step query results. This is called the ‘candidate set’. For each node in the candidate set, the post-processing step moves backwards through the location path expression—that is, the chain of ancestor nodes is obtained. (This may entail additional access to the database subtree store.) For each ancestor chain, the location path expression is tested in its entirety, to verify that the element node labels correspond, and then that each sequence of step predicates p_k1, . . . , p_kj evaluates to ‘true’. The post-processing algorithm is a ‘generate-and-test’ algorithm: for each element in the candidate set, a full path is generated by following parent links, and then this path is tested against the given location path expression in its entirety. The post-processing generator does not evaluate predicates for candidates whose ancestor chain fails to match the node label pattern, (e.g.) A/B/C/ . . . /T. For example, the location path query
 
A[p()]/B[q()]/C[r()]/@D
 
will be resolved as:
     1. Composer  224  takes step queries and forms the set of index search queries:
       Q 1 : element-child-descendant-query(“A”, “B”)   Q 2 : element-child-descendant-query(“B”, “C”)   Q 3 : element-attribute-query(“C”, “D”)   
       

     The first step query Q 1  corresponds to the canonicalized term A#/#B, the second step query Q 2  corresponds to the canonicalized term B#/#C, and the third step query Q 3  corresponds to the canonicalized term C#/@#D. Q 1  and Q 2  are ‘descendant-queries’, which means that the queries specify a search among the descendants of nodes matching the given pattern. In this example, the first step query ‘xqe:element-child-descendant-query(“A”, “B”)’ specifies a search among the descendants of B within subtrees containing the node pattern ‘A/B’.
     2. Intersector  226  receives a search of:
       search(and-query(Q 1 , Q 2 , Q 3 ), “C”).   
       

     A search is performed for the intersection of Q 1 , Q 2 , and Q 3 , which returns a sequence of nodes labeled C. The PostingLists for the canonicalized terms corresponding to Q 1 , Q 2 , and Q 3  are retrieved from index  213 , and then scanned for common subtree ids. The PostingList skip list structure is used to prune the search for common subtree ids. A PostingList block will be skipped over in the event that the ‘maxSubTreeID’ stored in the block is actually smaller than any of the currently smallest remaining subtree id in the other PostingLists.
     3. Post-processing:   

     For each node c labeled C, generate the ancestor path going back two steps, and check if grandparent(c)=A, parent(c)=B. If not, discard c, and loop around to processes the next node. If yes, then test the entire XPath expression
 
A[p — 11]...[p — 1a]/B[p — 21]...[p — 2a]/C[p — 31]...[p — 3a]/@D
 
by evaluating the predicate expressions from leftmost (highest) to rightmost (lowest) step, as specified in the XPath standard. In this example, the step tests include a test for an attribute node labeled ‘D’ following ‘C’.
 
       FIG. 10  illustrates a flow chart for a process for generating database  212  according to one embodiment. In step S 400 , relationships among elements in a document are computed. In step S 402 , step queries are generated from the relationships between the elements. For example, one-step, two-step, three-step, and four-step queries are generated from the relationship of elements. 
     In step S 404 , the step queries are reduced to their canonical form. In step S 406 , the process generates a hash key for each canonical form of the step queries. Additionally, in step S 408 , results for the step queries are generated from the relationship of elements. In one embodiment, the results represent one or more subtree IDs for the elements relating to each step query. 
     In step S 410 , the step query results and the corresponding hash keys are stored in database  212 . 
       FIG. 11  is a flow chart of a process for generating a result for query  119  according to one embodiment. In step S 500 , query  119  is received by XQE  200  at query processor  218 . In step S 502 , a query may be optimized. In step S 504 , the optimized query is then reduced into step queries. 
     In step S 506 , a hash key is generated for each of the step queries. In step S 508 , database  212  is accessed and step query results are retrieved using the calculated hash key. For example, a PostingList may be retrieved. 
     In step S 510 , the intersection of the step query results is taken and a query result is generated from the intersection. For example, results from the PostingList are subtree IDs. The method determines matching subtree IDs where the matching subtree IDs would include the step queries associated with the step query results. 
     In S 512 , the query result may be post-processed. In step S 514 , the query result is outputted. 
     An example using an embodiment of the present invention will now be described.  FIG. 12  depicts a PostingList  1000  that may be stored for the structure shown in  FIG. 8  according to one embodiment of the present invention. A plurality of step queries  1002  are shown. Each step query represents a combination of nodes shown in  FIG. 8  and one or more subtree IDs  1004  are associated with each step query  1002 . For example, the step query “c/a” is found in the subtrees “ 10 ” and “ 30 ”. 
     For discussion purposes, the relationships that cross subtrees are shown without any link nodes, for example, &lt;e&gt;→link node(c)→link node(e)→&lt;c&gt;is represented as &lt;e&gt;→&lt;c&gt;. Also, the upper node in the relationship is used to determine the subtree ID that is associated with step query. For example, the step query &lt;e&gt;→link node(c)→link node(e)→&lt;c&gt;is associated with subtree “ 40 ”. 
       FIG. 13  depicts PostingList  1000  with corresponding scores for each subtree ID according to one embodiment of the present invention. As shown, each step query  1002  and subtree ID  1004  pair has a score  1006  associated with it. Each score  1006  represents a numeric score that measures the relevance of step query  1002  to the step query in which it appears. In one embodiment, the score is computed by a function proportional to the number of occurrences of the term in the subtree divided by the total number of terms of any kind appearing in the subtree and may be normalized. 
       FIGS. 14A–14E  depict PostingList structures for each subtree according to one embodiment of the present invention.  FIG. 14A  shows step queries  1100  that represent each step query found in the subtree represented by subtree ID “ 10 ”. A frequency  1102  is shown for each step query  1100 . A score  1104  is also shown for each step query  1100 . For example, the step query “c/a” occurs twice in subtree  10  and has a score of 0.22. 
       FIG. 14B  shows step queries  1100  that represent each step query found in the subtree represented by subtree ID “ 20 ”.  FIG. 14C  shows step queries  1100  that represent each step query found in the subtree represented by subtree ID “ 30 ”.  FIG. 14D  shows step queries  1100  that represent each step query found in the subtree represented by subtree ID “ 40 ”.  FIG. 14E  shows step queries  1100  that represent each step query found in the subtree represented by subtree ID “ 50 ”. 
     Using the above PostingLists described in  FIGS. 12–14 , the following step query “b/c/a” may be queried. The query is broken down into the step queries of “b/c” and “c/a”. Table I shows values that may be retrieved for PostingList  1000 . 
                                     TABLE I                       Step Query   Subtree ID → Score   Subtree ID → Score                           b/c   20 → .08   50 → .18           c/a   10 → .22   30 → .18                        
The intersection of the subtree IDs for each step query is then taken. For example, the subtree IDs “ 20 ” and “ 50 ” are intersected with the subtree IDs “ 10 ” and “ 30 ”. The intersection of these IDs is empty.
 
     Although the intersection is empty, a further step may be taken to resolve the query. A query for step queries that may include link nodes (e.g., link node(c)) is then performed. Thus, step query results for the step query “&lt;b&gt;→link node (c)” may be retrieved. The results returned would be b/link node (c)=subtree ID  20 →(subtree ID  10 ); subtree ID  50 →(subtree ID  20 ); and subtree ID  50 →(subtree ID  40 ). The above means that a “b/c” step query is linked across the subtrees  20 / 10 ,  50 / 20 , and  50 / 40 . 
     Table II represents the new results including the linked step query results. 
     
       
         
               
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                   
                 Subtree ID → 
                 Subtree ID → 
                 Subtree ID → 
               
               
                 Step Query 
                 Score 
                 Score 
                 Score 
               
               
                   
               
             
             
               
                 b/c 
                 20 → .08 
                 50 → .18 
                   
               
               
                 c/a 
                 10 → .22 
                 30 → .18 
               
               
                 b/link node c 
                 20(10) 
                 50(20) 
                 50(40) 
               
               
                   
               
             
          
         
       
     
     The intersection of the three lists yields a set of candidate subtrees where the path b/c/a might occur, in this case, subtree ID  20 →subtree ID  10 . As shown in  FIG. 8 , the path b/c/a is found in subtrees  20  and  10 . The subtrees are then retrieved and examined to verify the presence or absence of the path b/c/a. The path is then returned as the result of the query. 
     Although scores were not used in the above example, in one embodiment, scores may be used to determine the relevance of step query results. If many results are returned, the scores may be used to determine which step query results may be processed first. For example, if a subtree ID has a high score, then it may be more likely that the subtree corresponding to the ID includes the elements of the query. Additionally, the subtree may be more relevant for the query. The scores may thus be used to prioritize processing and also to provide a list that represents the relevance of subtrees for a query. 
     In another example, system  200  may process results to determine if any false positives are returned for the results. Using the query, “c/a/b”, the following step queries are determined: “c/a” and “a/b”. Table III depicts an example PostingList. 
     
       
         
               
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                   
                 Subtree ID → 
                 Subtree ID → 
                 Subtree ID → 
               
               
                 Step Query 
                 Score 
                 Score 
                 Score 
               
               
                   
               
             
             
               
                 c/a 
                 10 → .22 
                 30 → .18 
                   
               
               
                 a/b 
                 10 → .22 
                 30 → .18 
                 50 → .27 
               
               
                   
               
             
          
         
       
     
     The intersection of the step query results for the two step queries yields the subtree IDs of “ 10 ” and “ 30 ”. The subtree fragments corresponding to the subtree IDs are then retrieved. Each subtree fragment includes both step queries. However, the path in a fragment may not include the full query. For example, the “c/a” fragment should end with the “a/b” fragment. The subtree fragments are then traversed to determine if a fragment includes the query.  FIG. 15A  shows a false positive match and  FIG. 15B  shows a positive match. As shown in  FIG. 15A , the “c/a” element does not connect directly to the “a/b” element. Thus, the fragment does not contain a “c/a/b” path. In  FIG. 15B , a positive is shown as the path “c/a/b” is found in the fragment. This path may be returned as the result of the query. 
     In one embodiment, XQE  200  may be used to search for text in documents  202 . A text search involves retrieving node sets (XML document fragments) that are relevant to a given set of terms. For example, a text search query may have the form: ‘return all Citation nodes whose text content is relevant to the phrase “knee surgery”.’ Complex search query results may be reduced to the intersection of step query results in much the same way that location path queries may be reduced to the intersection of step queries followed by the generate-and-test post-processing step. A search for a set of terms {term — 1, term — 2, . . . , term_n} or a phrase “term — 1 term — 2 . . . term_k” within the set of nodes with a given element A can be directly resolved by doing an index lookup for the terms: A#word(term — 1), A#word(term — 2), . . . , A#word(term_k), followed by an intersection of the results. For a phrase query, a post-processing step will verify that the terms appear contiguously in the subtrees. 
     XQE  200  indexes support full-text search across index  213 . XQE  200  includes a set of built-in functions which resolve a variety of full-text queries, with methods:
         (a) for constructing AND queries that specify a search within the intersection of any number of subsets specified by sub-queries,   (b) for constructing OR queries that specify a search within the union of any number of subsets specified by sub-queries,   (c) for constructing AND-NOT queries that specify a search within the set difference of two subsets specified by sub-queries,   (d) for constructing WORD queries that specify a search within elements whose text nodes contain a given phrase,   (e) for constructing ELEMENT queries that specify a search within the set of elements with a given QName,   (f) for constructing ELEMENT-VALUE queries that specify a search within the set of elements with a given QName whose full text value exactly matches a given phrase,   (g) for constructing ELEMENT-WORD queries that specify a search within the set of elements with a given QName whose text nodes contain a given phrase,   (h) for constructing ELEMENT-ATTRIBUTE queries that specify a search within the set of elements with a given QName which contain an attribute with a given QName,   (i) for constructing ELEMENT-ATTRIBUTE-VALUE queries that specify a search within the set of elements with a given QName which contain an attribute with a given QName, such that the attribute text exactly matches a given phrase,   (j) for constructing ELEMENT-ATTRIBUTE-WORD queries that specify a search within the set of elements with a given QName which contain an attribute with a given QName, such that the attribute text contains a given phrase,   (k) for constructing ELEMENT-CHILD queries that specify a search within the set of elements with a given QName that have a child with a given QName,   (l) for constructing ELEMENT-DESCENDANT queries that specify a search within the set of descendants of an element with a given QName,   (m) for constructing ROOT-ELEMENT-DESCENDANT queries that specify a search within the set of descendants of an element with a given QName whose parent is a document node with a given QName,   (n) for constructing ELEMENT-CHILD-DESCENDANT queries that specify a search within the set of descendants of an element with a given QName whose parent has a given QName,   (o) for constructing ELEMENT-ATTRIBUTE-DESCENDANT queries that specify a search within the set of descendants of an element with a given QName that has an attribute with a given QName,   (p) for constructing ELEMENT-ATTRIBUTE-VALUE-DESCENDANT queries that specify a search within the set of descendants of an element with a given QName that has an attribute with a given QName, such that the attribute text exactly matches a given phrase,   (q) for constructing URI queries that specify a search within the set of documents matching a given URI string.
 
A QName is a ‘Qualified Name’, which means a name of the form ‘prefix:name’, where prefix maps to some namespace URI, and name is any well-formed element or attribute name.
       

     In one embodiment, complex text search queries are assembled by composition of the ‘and-query’, ‘or-query’ and ‘and-not-query’ functions. The value of these functions is a ‘query value’, which represents a specification of a search pattern, which may be stored and evaluated at some subsequent point in the processing performed by XQE  200 . The query value represents a delayed evaluation—the query value specification determines a set of element sub-tree ids, but does not actually extract them from the database until passed to a function ‘search’. The function ‘search’ may take two arguments: a query value and an element QName, and evaluate the query specified by the query value argument returning a sequence of element sub-tree ids as specified by the QName argument. The QName argument may be an ancestor (or self) of the nodes returned by the query value specification. 
     In one embodiment, the sequence of nodes returned by the function search may be ordered by a ‘relevance’ score. The relevance of a node to the specified query is a complex function that depends on the frequency the query terms appear in the text of the query nodes, the frequency the query terms appear across the entire database, and the quality score attached to a given node. The quality score is further described in Linblad IV-A. 
     In one embodiment, XQE  200  calculates the relevance of a node relative to any of the previously described precomputed text queries as the stored ‘score’ value in the PostingList. Scores are composed through and-query&#39;s and or-query&#39;s by summation. The function and-query takes a sequence of any number of query values as an argument and returns a query value specifying a search matching all of the argument queries. The function or-query takes a sequence of any number of query values as an argument and returns a query value specifying a search matching any one of the argument queries. The function and-not-query takes two query value arguments and returns a query value specifying a search matching the first but not the second argument query. Complex queries may be built by successive application of and-query, or-query and and-not-query. For example,
         and-query(or-query((element-word-query(QName(“A”), “best”), element-word-query(QName(“A”), “worst”))), element-word-query(“A”, “times”)),
 
specifies a query for elements labeled “A”, containing the term “times” and either one of the terms “best” or “worst”. In addition, each of the query value functions can accept an argument specifying a relative weight for the query as a constituent of the composed query. For example,
   and-query(or-query((element-word-query(QName(“A”), “best”, 0.7), element-word-query(QName(“A”), “worst”, 0.4))), element-word-query(“A”, “times”, 0.9))
 
specifies a query for elements labeled “A”, containing the term “times” and either one of the terms “best” or “worst”, with the appearance of “worst” given relative weight 0.4, the appearance of “best” a relative weight of 0.7, and the appearance of “times” given a relative weight of 0.9. The relative weights are used when assigning an ordering to the result of a query.
       

     Embodiments of the present invention provide methods for generating a pre-computed index that is used for generating a result for a query. Step queries are pre-computed and the results to these step queries generated and stored in the index along with the step queries. The step queries include a set of elements that are related in a parent-child relationship and may be used to generate a result for a query. Embodiments of the present invention receive a query and break the query into multiple step queries using elements from the path of the query. Results from these step queries are then retrieved from the index and the intersection of the retrieved results is taken to generate a result for the query. The result yields a location or elements that satisfy the query. 
     In one embodiment, relationships among elements in XML documents are computed and possible step queries that may be generated from the XML documents are computed. Because these step queries are pre-computed, XQueries that include the pre-computed step queries are satisfied in an efficient manner. Instead of traversing the hierarchical structure of the XML document on a node-by-node basis to find an element of the document, an index of pre-computed results for step-queries is used to generate a result for the query. 
     The above description is illustrative but not restrictive. Many variations of the invention will become apparent to those skilled in the art upon review of the disclosure. The scope of the invention should, therefore, be determined not with reference to the above description, but instead should be determined with reference to the pending claims along with their full scope or equivalents.