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Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Matching Tree Patterns on Partial-trees Optimizing Tree-Pattern Matching Shachar Harussi Supervision of Prof. Amir Averbuch September 1,

  1. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Matching Tree Patterns on Partial-trees Optimizing Tree-Pattern Matching Shachar Harussi Supervision of Prof. Amir Averbuch September 1, 2011 Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  2. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur 1 Motivation: Graph querying 2 Background: tree patterns 3 Partial trees - holistic divide and concur Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  3. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Outline 1 Motivation: Graph querying 2 Background: tree patterns 3 Partial trees - holistic divide and concur Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  4. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Motivation Everything is a graph. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  5. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Motivation(cont.) We need to query everything. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  6. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Lets take a picture A picture is a graph. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  7. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Lets take a picture A picture is a graph. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  8. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Holistic approach Given a graph pattern. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  9. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Holistic approach Given a graph pattern. And a graph data, Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  10. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Holistic approach Given a graph pattern. And a graph data, The solution is O O. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  11. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur But Holistic is hard A Problem: Holistic pattern matching is NP-hard. Even subgraph isomorphism problem [8] is hard. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  12. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur But Holistic is hard A Problem: Holistic pattern matching is NP-hard. Even subgraph isomorphism problem [8] is hard. A Solution: divide and concur. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  13. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local is easy Divide the pattern a local patterns P i , Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  14. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local is easy Divide the pattern a local patterns P i , And local data D i . Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  15. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local is easy Divide the pattern a local patterns P i , And local data D i . Partial solutions O O. Strings matching is fast O ( P i × D i ) Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  16. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local is easy Divide the pattern a local patterns P i , And local data D i . Partial solutions O O. Strings matching is fast O ( P i × D i ) Join (Concur) Final solution O O. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  17. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur So local approach is perfect ? The answer is NO Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  18. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur So local approach is perfect ? The answer is NO The concur is a Pyrrhic victory - i.e. the join costs. But lets focus on trees. Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  19. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Outline 1 Motivation: Graph querying 2 Background: tree patterns 3 Partial trees - holistic divide and concur Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  20. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Tree Data Model v 1 a v 2 ‘ Tree pattern ’ is a tree b v 3 v 4 c d Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  21. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur The local approach problem an example query : ‘/a/b[/c]/d’ v 1 a v 2 v 4 v 7 b b b v 6 v 3 v 5 v 8 c c d d Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  22. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur The local approach problem an example query : ‘/a/b[/c]/d’ 1. path1 (‘/a/b/c’): v 1 ( v 1 , v 2 , v 3 ), ( v 1 , v 4 , v 5 ) a v 2 v 4 v 7 b b b v 6 v 3 v 5 v 8 c c d d Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  23. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur The local approach problem an example query : ‘/a/b[/c]/d’ 1. path1 (‘/a/b/c’): v 1 ( v 1 , v 2 , v 3 ), ( v 1 , v 4 , v 5 ) a 2. path2 (‘/a/b/d’): ( v 1 , v 4 , v 6 ), ( v 1 , v 7 , v 8 ) v 2 v 4 v 7 b b b v 6 v 3 v 5 v 8 c c d d Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  24. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur The local approach problem an example query : ‘/a/b[/c]/d’ 1. path1 (‘/a/b/c’): v 1 ( v 1 , v 2 , v 3 ), ( v 1 , v 4 , v 5 ) a 2. path2 (‘/a/b/d’): ( v 1 , v 4 , v 6 ), ( v 1 , v 7 , v 8 ) 3.joins: v 2 v 4 v 7 ( v 1 , v 2 , v 3 , ) b b b ( v 1 , v 4 , v 5 , ) ( v 1 , v 4 , , v 6 ) v 6 v 3 v 5 v 8 ( v 1 , v 7 , , v 8 ) c c d d Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  25. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur The local approach problem an example query : ‘/a/b[/c]/d’ 1. path1 (‘/a/b/c’): v 1 ( v 1 , v 2 , v 3 ), ( v 1 , v 4 , v 5 ) a 2. path2 (‘/a/b/d’): ( v 1 , v 4 , v 6 ), ( v 1 , v 7 , v 8 ) 3.joins: v 2 v 4 v 7 ( v 1 , v 2 , v 3 , ) b b b ( v 1 , v 4 , v 5 , ) ( v 1 , v 4 , , v 6 ) v 6 v 3 v 5 v 8 ( v 1 , v 7 , , v 8 ) c c d d 4. answer : ( v 1 , v 4 , v 5 , v 6 ) Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  26. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local structural-indexes Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  27. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local structural-indexes Tree representation that is: small, enables querying Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  28. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local structural-indexes Tree representation that is: small, enables querying Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

  29. Outline Motivation: Graph querying Background: tree patterns Partial trees - holistic divide and concur Local structural-indexes Tree representation that is: small, enables querying The current indexes (Dataguide [5],1-index [3]) are: Shachar Harussi Supervision of Prof. Amir Averbuch Matching Tree Patterns on Partial-trees

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