Keyword proximity search in xml trees andrada astefanoaie - presentation
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This document discusses algorithms for keyword proximity search in XML trees. It presents two problems: identifying all minimum connecting trees (MCTs) that connect keyword nodes, and identifying lowest MCTs whose root is not an ancestor of another MCT root. For indexed XML data, it proposes a nested loop algorithm and a more efficient stack-based algorithm. For unindexed data, it adapts the stack algorithm to perform in one pass over the data tree. Experimental results show the stack-based algorithms generally outperform nested loops algorithms.
![Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview
Notation Keyword Proximity Search
in XML Trees
DMCT
v1, . . . , vm Є T.
Distance MCT (DMCT) TD=d(TM) of the MCT TM of nodes v1, . . . , vm → the minimum node-labeled
and edge-labeled tree such that:
TD contains v1, . . . , vm
TD contains the LCAs u1, . . . , uk
of any pair of nodes (vi, vj)
where vi , vj Є [v1, . . . , vm], i≠ j
edge labeled with l between
any two distinct nodes n, n’ Є
{v1,...,vm, u1, . . . ,uk} if there is a
path of length l from n’ to n in
TM and the path does not
contain any node n’’ Є { u1, . . . ,
um} other than n and n’.](https://image.slidesharecdn.com/keywordproximitysearchinxmltrees-andradaastefanoaie-presentation-120715051324-phpapp02/85/Keyword-proximity-search-in-xml-trees-andrada-astefanoaie-presentation-7-320.jpg)
Keyword proximity search in xml trees andrada astefanoaie - presentation
- 1. Keyword Proximity Search in XML Trees Andrada Astefanoaie XML and Database Systems SS 2010
- 2. Outline I. Introduction II. Framework III. Algorithms:Indexed XML Data Keyword Proximity Search IV. Processing Unindexed XML DATA in XML Trees V. Experimental Evaluation VI. Overview
- 3. Introduction - Framework - Algorithms:Indexed XML Data – Processing Unindexed XML Data - Experimental Evaluation - Overview Keyword Search Keyword Proximity Search in XML Trees Keyword search user-friendly information discovery technique extensively studied for text documents. Keyword proximity search well-suited to XML documents
- 4. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Notation Keyword Proximity Search in XML Trees XML DOCUMENT directed tree with labeles - labled with λ(v), a tag - 4-tuple: id(v) start and end correspond to the first and the final times the node is v visited in a depth-first traversal of the XML tree, depth is the depth of the node from the root of the tree. - if v is a leaf, it has a string value val(v) that contains a list of keywords set of keywords k1,. . . , km. keyword query returns a compact representation of the set of trees that connect the nodes that contain the keywords
- 5. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Notation Keyword Proximity Search in XML Trees r c1 s1 s2 s3 p2 p5 p6 p1 p3 p4 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10
- 6. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Notation Keyword Proximity Search in XML Trees Definition minimum connecting tree (MCT) of nodes v1,. . . ,vm of a tree → the minimum size subtree that connects v1, . . . ,vm. root of the tree → the lowest common ancestor (LCA) of the nodes v1, . . . ,vm. Examples: r r MCTs for the query MCTs for the query “Tom, Harry” c1 “Tom, Dick, Harry” c1 s1 s2 s3 s1 s2 s3 p1 p2 p4 p5 p6 p1 p2 p3 p4 p5 p6 p3 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a1 a2 a3 a7 a8 a4 a5 a6 a9 a10
- 7. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Notation Keyword Proximity Search in XML Trees DMCT v1, . . . , vm Є T. Distance MCT (DMCT) TD=d(TM) of the MCT TM of nodes v1, . . . , vm → the minimum node-labeled and edge-labeled tree such that: TD contains v1, . . . , vm TD contains the LCAs u1, . . . , uk of any pair of nodes (vi, vj) where vi , vj Є [v1, . . . , vm], i≠ j edge labeled with l between any two distinct nodes n, n’ Є {v1,...,vm, u1, . . . ,uk} if there is a path of length l from n’ to n in TM and the path does not contain any node n’’ Є { u1, . . . , um} other than n and n’.
- 8. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Notation Keyword Proximity Search in XML Trees GDMCT A Grouped DMCT of a tree T is a labeled tree where edges are labeled with numbers and nodes are labeled with lists of node ids from T. DMCT D Є GDMCT G if D and G are isomorphic. Assuming that f is the mapping of the nodes of D to the nodes of G, which induces a corresponding mapping, also called f, of the edges of D to the edges of G, the following must hold: nD is a node of D, nG is a node of G and f(nD)=nG, then the label of nG contains the id of nD. eD is an edge of D, eG is an edge of G and f(eD) = eG, then the label of eD and the label of eG are the same number.
- 9. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Problems Keyword Proximity Search in XML Trees Problem 1 : All GDMCTs Problem Query K Result “Tom, Harry” 5 3
- 10. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Problems Keyword Proximity Search in XML Trees Problem 2 : Lowest GDMCTs Problem Query K Result “Tom, Harry” 5 3
- 11. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Nested Loop Algorithm The nested loops algorithm (NL) for the case of indexed XML Examples of some entries in the data operates over separate lists of nodes, L(k), one for each master index for our tree: query keyword, k, to identify the GDMCTs whose sizes are no more than the user-provided threshold, K. Master index inverted index a hash table list L(k) each node n has path-id (the list of node ids along the path from the root of T to n)
- 12. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Nested Loop Algorithm checks all combinations of nodes from the keyword lists. for each combination computes an MCT (minimum connecting tree) merges the resulting MCT into the list of result GDMCTs, if its size is within the user-specified threshold.
- 13. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Nested Loop Algorithm For example: Query: “Tom, Harry” and K=3, NL examine the 12 node-pairs 12 MCTs determine 2 of them meet the threshold(K) return 2 GDMCTs:
- 14. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Nested Loop Algorithm Inefficienty: NL checks all the combinations of nodes from the keyword lists The grouping of the results into GDMCTs is not lightly integrated with the algorithm and a lookup to the array R is required for each relevant MCT found.
- 15. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Index Structure and Algorithm. The stack-based algorithm for computing GDMCTs on indexed XML data operates over lists of nodes, two for each query keyword. Indexing by keyword master index contains 2 lists o L(k) of the nodes of T that contain k in T and o Ld(k) of the ancestors of nodes in L(k).
- 16. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Index Structure and Algorithm. For example the entries for Tom, Dick and Harry are:
- 17. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Index Structure and Algorithm. This is the high-level description of the SA. It describes how the selected list of nodes is traversed in a depth-first manner and the nodes are pushed and popped from the stack.
- 18. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Index Structure and Algorithm. novel part of the SA algorithm processing and bookkeeping performed at each stack operation
- 19. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Index Structure and Algorithm. Functions that are called from POP(S)
- 20. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Illustrative Example Query: “Tom, Harry” K=3 Master index lists: The intersection of the lists:
- 21. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Illustrative Example Master index lists: Intersection of the La Query: “Tom, Harry” K=3 Some of the initial stack states of the execution of the Stack Algorithm: 1. 2. 3.
- 22. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Illustrative Example Master index lists: Intersection of the La Query: “Tom, Harry” K=3 Some of the initial stack states of the execution of the Stack Algorithm: 4. 5. 6.
- 23. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview All GDMCTs: Keyword Proximity Search in XML Trees Stack-Based Algorithm Illustrative Example Master index lists: Intersection of the La Query: “Tom, Harry” K=3 Some of the initial stack states of the execution of the Stack Algorithm: 7. 8. 9. Entries from the lists continue being examined, new GDMCTs are created and pruned until all the answers are output. ...
- 24. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Lowest GDMCTs: Keyword Proximity Search in XML Trees Stack- Based Algorithm The key observation is that once we output the GDMCTs of a node u, none of the ancestors of u in the stack can be LCAs of returned GDMCTs; hence, we can remove all of them from the stack! Specifically, we can add the following lines after line 5:
- 25. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview LCAs: Keyword Proximity Search in XML Trees Stack- Based Algorithms The Stack Algorithm can also be easily modified to solve the All LCAs Problem and the Lowest LCAs Problem, where the user is not interested in the GDMCTs, but only in the LCA nodes. o First, Merge(.) could be simplified, no merging of GDMCTs would need to be done, and line 33 could be replaced by: o Second, we can output an LCA early when the first GDMCT (with all keywords) is computed for that node (in Procedure CreateNewGDMCTs(.)), instead of waiting until the node is popped from the stack.
- 26. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Complexity Keyword Proximity Search in XML Trees Analysis Total number of GDMCTs Worst case: the number of DMCTs and of GDMCTs = exponential on the number of keywords. Under reasonable assumptions, the worst-case number of GDMCTs is smaller than that of DMCTs Complexity of Finding Isomorphic GDMCTs Given this canonical representation prezented in this chapter, one can linearize the GDMCTs in an XML-like nested representation with start and end tags, obtained from the node annotations. Theorem 1. The time complexity of SA is O( L K (i 1 L(ki ) ) 2 ) m
- 27. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Processing Keyword Proximity Search in XML Trees Unindexed XML Data Both the NL Algorithm and the SA have adaptations to work without index lists by doing a single pass over the data tree. The streaming version of the Stack Algorithm following changes to the Stack Algorithm SA(k1,..km, K):
- 28. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Experimental Keyword Proximity Search in XML Trees Evaluation Parameters affecting the performance of the presented algorithms: 1) the value of K denoting the threshold, 2) the number m of keywords, 3) the size of the data set. Tests show that usually the algorithms based on the Stack Algorithm have better results than the Nested Loops Algorithms both in the Indexed and Unindexed data.
- 29. Introduction - Framework - Algorithms:Indexed XML Data - Processing Unindexed XML Data - Experimental Evaluation - Overview Overview Keyword Proximity Search in XML Trees There were presented two main problems: 1) identifying and presenting in a compact manner all MCTs which explain how the keywords are connected 2) identifying only MCTs whose root is not an ancestor of the root of another MCT. There are presented solutions: 1) when the XML data has been preprocessed and relevant indices have been constructed - Nested Loop Algorithm - Stack Algorithm 2) when the XML data has not been preprocessed, i.e., the XML data can only beprocessed sequentially. Benefits of the algorithms are shown by the Experimental Evaluation
- 30. Resource Name Keyword Proximity Search in XML Trees Vangelis Hristidis, Nick Koudas, Yannis Papakonstantinou and Diverish Srivastava Authors IEEE Transactions on Knoledge and Data Engineering Publication Vol 18, No 4, APRIL 2006
- 31. Keyword Proximity Search in XML Trees Thank you!