1. Structural Joins: A Primitive for Efficient XML Query Pattern Matching Shurug Al-Khalifa, H. V. Jagadish, Nick Koudas, Jignesh M. Patel, Divesh Srivastava, Yuqing Wu Presented by Parag Abhyankar 08305017

2. 2 Introduction XQuery Specify patterns of Selection Predicate having Tree Structural Relationship.  e.g. book[title = ‘XML’] // author[. = ‘jane’] The primitive tree structured relationships  Parent-child : (book, title), (title,XML), (author, jane)‏  Ancestor-descendant : (book, author)‏ Finding all occurrences of these relationships is a core operation for XML query processing.

3. 3 Representing XML Elements : (Background)‏ Element: (DocId, StartPos : EndPos, LevelNum) String: (DocId, StartPos, LevelNum) Inspired from 'Multi-Predicate Merge Join' by Zang

4. 4 Background continued.. Element E1(D1,S1:E1,L1)‏ Element E2(D2,S2:E2,L2)‏ If D1=D2, S1<S2 and E2<E1  E1-E2 is ancestor-descendant If D1=D2, S1<S2, E2<E1 and L1+1=L2  E1-E2 is parent-child

5. 5 Structural Joins Join Algorithms for matching Structural Relationship  tree-merge and stack-tree Input: Lists of tree nodes sorted by (DocId, StartPos)‏ Output: Lists of sorted results joined according desired structural relationship. Use in XML Query Pattern matching  Query Tree Pattern  decompose  binary structural relationships.  Match each relationship with XML database  ‘Stitching’ together basic matches

6. 6 Tree-Merge Join (O/p Sorted Ancestor/Parent order)‏ AList and DList lists of potential ancestors and descendants in sorted order. For every node in AList do  Skip all unmatchable d's (d starts before a)‏  Output pair (a,d) till a ends after d.

7. 7 Example Alist={Title_1} Dlist={Book_1, XML_1, Jane_1} Title_1  Skips Book_1 as it starts before Title_1.  Pairs with XML_1  Do not consider Jane_1 as it ends after Title_1. Book Author Jane Title XML AList Title_1 DList Book_1 XML_1 Jane_1

8. 8 Tree-Merge Join Detail Algorithm (O/p Sorted Ancestor/Parent order)‏

9. 9 Example a i pairs with each d j where i <= j <= 2i-1 Worst Case scenario. Complexity: O(|AList| + |DList| + |OutputList|)‏

10. 10 Tree-Merge Join (O/p Sorted Descendants order)‏ AList and DList lists of potential ancestors and descendants in sorted order. For every node in DList do  Skip all unmatchable a's (a ends before d starts)‏  Output pair (a,d) till a starts before d starts.

11. 11 Example Alist={Book_1, Title_1} Dlist={Book_1, XML_1, Jane_1} Book_1  doesn't have any matching a. XML_1  Pairs with Book_1, Title_1 Jane_1  Pairs with Book_1  Do not consider Title_1 (as Title_1 starts before Jane_1)‏ Book Author Jane Title XML AList Book_1 Title_1 DList Book_1 XML_1 Jane_1

12. 12 Tree-Merge Join Algorithm (O/p Sorted Descendent/Child order)‏

13. 13 Example d i pairs with a i and a 0 Worst Case scenario.

14. 14 Stack-Tree Desc. (O/p sorted by Descendants)‏ Stack Contains Elements that can be ancestor of remaining ds Consider elements from Alist and Dlist one by one  If top can not be ancestors, POP it out.  If new 'a' has potential to be ancestor add to Stack  Else new 'd' will pair with all elements for Stack (Bottom to Top )‏

15. 15 Stack-Tree Desc. (O/p sorted by Descendants)‏

16. 16 Example AList = {a1,a2,a3,…,an} DList = {d1,d2,d3,….d 2n } a  a1 d  d1 Stack Only a i s can go on Stack

17. 17 Example continued.. AList = {a2,a3,…,an} DList = {d1,d2,d3,….d 2n } As a starts before d a1 goes to stack a  a2 d  d1 a1 Stack

18. 18 AList = {a2,a3,…,an} DList = {d2,d2,d3,….d 2n } As d starts before a d1 pairs with all elements from Stack a  a2 d  d2 Example continued.. a1 Stack

19. 19 AList = {a3,a3,…,an} DList = {d2,d2,d3,….d 2n } As a starts before d a2 goes to stack a  a3 d  d2 Example continued.. a2 a1 Stack

20. 20 AList = {a3,a3,…,an} DList = {d2,d2,d3,….d 2n } As d starts before a d2 pairs with all elements from Stack a  a3 d  d3 Example continued.. a2 a1 Stack

21. 21 AList = {} DList = {d n+2,….d 2n } d  d n+2 d n+2 will pop a n As a n ends before d n+2 Top  a n-1 Example continued.. a n-1. a2 a1 Stack dn+2

22. 22 Stack-Tree Anc. (O/p sorted by Ancestor)‏ Tricky: As join with top of stack can’t be added to o/p until join to it’s ancestor is added to o/p. two lists are associated with each node on the stack:  self-list is a list of result elements from the join of this node with appropriate DList elements.  inherit-list is a list of join results involving AList elements that were descendants of the current node on the stack.

23. 23 Stack-Tree Anc. (O/p sorted by Ancestor)‏

24. 24 Example AList = {a1,a2,a3,…,an} DList = {d1,d2,d3,….d 2n } a  a1 d  d1 Stack Only a i s can go on Stack

25. 25 Example continued.. AList = {a2,a3,…,an} DList = {d1,d2,d3,….d 2n } As a starts before d a1 goes to stack a  a2 d  d1 a1 Stack

26. 26 AList = {a2,a3,…,an} DList = {d2,d2,d3,….d 2n } As d starts before a d1 pairs with all elements from Stack and added to their self-list a  a2 d  d2 Example continued.. a1 Stack SL= d1 IL=

27. 27 AList = {a3,a3,…,an} DList = {d2,d2,d3,….d 2n } As a starts before d a2 goes to stack a  a3 d  d2 Example continued.. a2 a1 Stack SL= d1 IL=

28. 28 AList = {a3,a3,…,an} DList = {d2,d2,d3,….d 2n } As d starts before a d2 pairs with all elements from Stack and added to their self-list a  a3 d  d3 Example continued.. a2 a1 Stack SL= d1, d2 IL= SL= d2IL=

29. 29 AList = {} DList = {d n+2,….d 2n } d  d n+2 d n+2 will pop a n a n ’s SL appended to IL and IL appended to a n-1 ’s SL Top  a n-1 Example continued.. a n-1. a2 a1 dn+2 SL= d1,d2.. SL= d2,d3… SL= dn-1IL=(an-dn)‏.. IL= The Last node coming out of Stack will append IL to OutputList

30. 30 Experimental Evaluation Results –STJ-D outperforms other algorithms Single pass over i/p nodes, No intermediate file writes –STJ-A showed better performance than TMJ-A, TMJ-D –Performance of STJ-A is comparable with TMJs when result size is large. Writing to intermediate files