Bottom-up Evaluation of XPath Queries Stephanie H. Li Zhiping Zou

Outline  Overview of XPath  Motivation  Algorithms : bottom-up evaluation  Design and implementation

Introduction- Overview  Overview of Xpath XPath is a querying language and is designed for addressing nodes of XML documents. Data model Syntax Expressions  Location paths  Operators  Functions Evaluation(context)

Data Model  Data Model XML document = tree of nodes 7 kinds of nodes: Element Attribute Text Namespace Processing-instruction Comment Document (root) nodes.

Data Model(Example) r a bb The root node The root element b b

Expression  XPath uses expressions to select nodes from XML documents  The main types of expressions are Location Paths, Functions and operators

Location Paths  Although there are many different kinds of XPath expressions, the one that’s of primary use in Java programs is the location path.  Location Path: /child::movies/child::movie[position()=5] step axis nodetest predicate location path

Location Step  Axis::Nodetest[predicts] Axis: chooses the direction to move from the context node Node test: determines what kinds of nodes will be selected along that axis Predicts: further filter the node-set.

XPath Axis  Axis---main navigator for a XML doc ancestor : nodes along the path to the root ancestor-or-self : same but including the context node child : children of the context node descendant : descendants of the context node descendant-or-self : same but including the context node following : nodes after the context node in document order, excluding descendants following-sibling : following sibling of the context node parent : the parent of the context node preceding : nodes before the context node in document order,excluding ancestors preceding-sibling : preceding sibling of the context node

Node Test  Node Type test Example T(root()) = {r}, T(element()) = {a; b1; : : : ; b4} T(element(a))= {a} T(element(b)) = {b1; : : : ; b4}  Node Name test Element node name

Operators and Functions  Arithmetic Ops  Ops for comparisons and boolean logic: {, =,=,!=} {or, and}  Functions Position() Last()

Xpath Query Evalutation  Query evaluation is a major algorithmic problem Main construct is the expression Each expression is evaluated to yield an object one of these four types: Node-set (an unordered collection of nodes without duplicates ) Boolean(true or false) Number(a floating-point number ) String

Context  All XPath expressions are evaluated w.r.t. a Context,which consists of A context node A context position(int) A context size(int)  The input context for query evaluation is chosen by the user.

Motivation  Claim: The way XPath is defined in W3C XPath recommendation motivates an inefficient implementation (exponential-time).  This paper propose more efficient way (polynomial-time)

Basic query evaluation strategy Procedure process-location-step(n 0, Q) /* n 0 is the context node; query Q is a list of location steps */ Begin node set S := apply Q.first to node n 0 ; if (Q.tail is not empty) then for each node n ∈ S do process-location-step(n, Q.tail); End Time(|Q|) = |D| * Time(|Q|-1) or |D| |Q| when |Q| > 0 1 when |Q| = 0 The algorithm recursively evaluates each remaining step for each matching node of the current step

Xpath Evaluate in PTime  Theorem: Let e be an arbitrary XPath expression. Then, for context node x, position k, and size n, the value of e is v, where v is the unique value such that ∈ E↑[e]  The main principle that the paper propose to obtain an XPath evaluation algorithm with PTime complexity is the notion of a context-value table(CVT)

Context-value table Principle  Given an expression e, the CVT of e specifies all valid combinations of contexts c and values v, s.t. e evaluates to v in context c  Such a table for expression e is obtained by first computing the CVTs of the direct subexpressions of e and then combining them into the CVT for e.  The size of each of the CVTs has a polynomial bound  Each of the combination steps can be effected in PTime  Thus, query evaluation in total under our principle also has a PTime bound

Bottom-up evaluation of XPath

Algorithm (Bottom-up algorithm for XPath) Input: An XPath query Q; Output: E↑[Q] Method: Let Tree(Q) be the parse tree of query Q; R:=Ø; For each atomic expression l ∈ leaves(Tree(Q)) do compute table E↑[l] and add it to R; [Note: we use JDom to do this] While E↑[root(Tree(Q))]! ∈ R do Begin take an Op(l1,…ln) nodes(Tree(Q)) s.t. E↑[l1],… E↑[ln] ∈ R; compute E↑[Op(l1,…ln)] using E↑[l1],…, E↑[ln]; add E↑[Op(l1,…ln)] to R; End; Return E↑[root(Tree(Q))] By a bottom-up algorithm we mean a method of processing XPath while traversing the parse tree of the query from its leaves up to its root.

Bottom-up evaluation of XPath  Example XML : Alan Turing computer scientist mathematician cryptographer href=" Richard M. Feynman physicist Playing the bongoes

Example: XML Doc Tree

Example: XPath Query tree Parse tree XPath query: descendant:: profession/following-sibling::*[position()!= last()]

Example: Evaluate subexpressions

Design and Implementaion  Environment Java,JDK1.5.0 Jdom1.0 XPath1.0 Features: Only Element nodes are queried Not support abbreviated xpath expressions Not support format of location steps in predicts.

System Structure Query Parser (Parser.java BinaryTree.java,Node.java) User input (MyDriver.java) Query tree Evaluator( QueryEval.java) JDom XML parser (org.jdom.input.SAXBuilder) Context value tables (ContextValTable.java and others) XML document tree Result for the full xpath query XML file Query Context node

Conclusion  XPath query evaluation algorithm that runs in polynomial time with respect to the size of both the data and the query (linear in the size of queries and quadratic in the size of data)  No optimization, strictly coheres to the specification given in the paper

References  G. Gottlob, C. Koch, and R. Pichler. "Xpath Processing in a Nutshell". In Proceedings of the 19th IEEE International Conference on Data Engineering (ICDE'03), Bangalore, India, Mar  G. Gottlob, C. Koch, and R. Pichler. "Efficient Algorithms for Processing XPath Queries". In Proceedings of the 28th International Conference on Very Large Data Bases (VLDB'02), Hong Kong, China, Aug  G. Gottlob, C. Koch, and R. Pichler. "XPath Query Evaluation: Improving Time and Space Efficiency". In Proceedings of the 19th IEEE International Conference on Data Engineering (ICDE'03), Bangalore, India, Mar 