1. 1 The MV3R-Tree: A Spatio- Temporal Access Method for Timestamp and Interval Queries Yufei Tao and Dimitris Papadias Hong Kong University of Science and Technology Present by Guangyue Jia

2. 2 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

3. 3 Motivation Spatio-tempral queries are common. –Data: (tid, sid, x1, y1, x2, y2, t1, t2) –Query: space restriction + time restriction Timestamp (or timeslice) query and interval query. Process both timestamp and interval query efficiently.

4. 4 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

5. 5 Related works MVB-tree: –Multi-version B-tree HR-tree –Historical R-tree 3D R-tree –3 Dimension R-tree

6. 6 MVB-tree Each entry has the form: –Insertions and deletions only happen at the current time. An entry called alive at a timestamp t if t start <=t<t end Multiple roots and each root has a jurisdiction interval: –Minimum bounding lifespan of all the entries in the root. Either none or b · p version entries are alive for each timestamp t and each node except the roots. –Ensures that entries alive at the same timestamps are mostly grouped together. Example of MVB-tree p version =1/3 b=6

7. 7 Overflow Insertion is carried out as B-tree except overflows. Weak version overflow: block overflow. And it cause version split. number of live entries in a new node must be in the range [b·p svu, b·p svo ]. Strong version overflow: number of live entries exceeds b·p svo. Strong version overflow cause key split.

8. 8 Version split Example of MVB-tree Example of block overflow and version split Description: 1, When weak version overflow. 2, All live entries are copied to a new node. 3, t start modified to the current time. 4, t end of the live entries is changed from * to the current time. 5, create data redundancy. Example: 1, insert at time 4. 2, A weak version overflow. 3, create new node D and copy the live entries to it. 4, all t start are set to be 4 5, A ”dies”, all * are replaced by 4.

9. 9 Underflow Deletion is carried out as B-tree except underflows. Weak version underflow: number of live entries lower than b·p version Strong version underflow: number of live entries becomes lower than b·p svu. Underflow: copy sibling node using only its live entries.

10. 10 Mergence and key split Root ABC 1, delete entry at timestamp 4. 2, B weak version underflow since only entry is alive. 3, copy live entries from sibling node C to C´. 3, insert into C´cause strong version overflow. 4, key split and node D and E are created. p version =p svu =1/3 p svo =5/6

11. 11 Mergence and key split Root ABC 1, delete entry at timestamp 4. 2, B weak version underflow since only entry is alive. 3, copy live entries from sibling node C to C´. 3, insert into C´cause strong version overflow. 4, key split and node D and E are created. p version =p svu =1/3 p svo =5/6

12. 12 Mergence and key split Root ABC 1, delete entry at timestamp 4. 2, B weak version underflow since only entry is alive. 3, copy live entries from sibling node C to C´. 3, insert into C´cause strong version overflow. 4, key split and node D and E are created. C´ p version =p svu =1/3 p svo =5/6

13. 13 Mergence and key split Root ABC 1, delete entry at timestamp 4. 2, B weak version underflow since only entry is alive. 3, copy live entries from sibling node C to C´. 3, insert into C´cause strong version overflow. 4, key split and node D and E are created. C´ p version =p svu =1/3 p svo =5/6

14. 14 Mergence and key split Root ABC 1, delete entry at timestamp 4. 2, B weak version underflow since only entry is alive. 3, copy live entries from sibling node C to C´. 3, insert into C´cause strong version overflow. 4, key split and node D and E are created. D E p version =p svu =1/3 p svo =5/6

15. 15 Historical R-tree The structure maintains an R-tree for each timestamp. Good for timestamp queries. Need a lot of space. Example of an HR-tree

16. 16 3D R-tree Good for time interval queries A timestamp query in 3D R-tree

17. 17 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

18. 18 MV3R-tree Intruduction MVR-tree Insertion and overflow handling in MVR- tree Reinsertion Deletion and underflow handling in MVR- tree Auxiliary 3D R-tree Query processing with MV3R-tree

19. 19 Introduction An idea to deal with both timestamp and interval queries. MVR-tree + 3DR-tree Overview of an MV3R-tree

20. 20 MVR-Tree Multi-version R-tree. Can contain multiple R-trees. Each entry has the form A small MVR-tree with height 2 b=3 p version =1/3 1, A to G are object boxes. 2, H, I, and J are leaf nodes. 3, C, I and K are alive (unbounded).

21. 21 Insertion and overflow handling in MVR-tree Not overflow in intermediate nodes: –Set t start to the current time. Overflow in intermediate nodes: Insertion in intermediate nodes

22. 22 Insertion and overflow handling in MVR-tree Not overflow in leaf nodes: –Set t start to the current time. Overflow in leaf nodes: Insertion in leaf nodess

23. 23 Reinsertion Any leaf node of MVR-trees can store a reinserted entry. Different from MVB-tree. If general key split fails.

24. 24 Deletion and underflow handling in MVR-tree Not underflow in intermediate nodes: –Modify t end from * to the current time. Underflow in intermediate nodes: –Set t end of its live entries to current time. All entries are dead. –Reinsert these entries to the most recent logical R-tree after setting t start =current time. –MVB-tree handle underflows by merging with sibling nodes.

25. 25 Deletion and underflow handling in MVR-tree Not underflow in leaf nodes: –Modify t end from * to the current time. Underflow in leaf nodes: –First attempt to borrow a live entry from a sibling node. –entry reinsertion if the heuristic fails (cause redundancy). Borrowing a live entry from a sibling node 1, At timestamp 2, entry A1 is deleted. 2, node A weak version underflow. 3, version condition must still be satisfied in B after removal. (removal of B2 or B3 can cause weak version underflow for timestamp 1.) b=8, Pversion=1/3

26. 26 Auxiliary 3D R-tree In order to process long time interval queries. 3D R-tree is built on the leaves of the MVR-tree. Whenever a leaf node of the MVR-tree is updated, the change is propagated to its entry in the 3D R-tree.

27. 27 Query processing with MV3R-tree Choose between 3D R-tree and MVR-tree. –3D R-tree is preferable for long time interval queries. –MVR-tree is good for timestamp queries. –Threshold is given for short time interval queries. When use MVR-tree, it choose the MVR-trees whose roots´jurisdiction interval cover the queried timestamp or interval. Duplicate visits for time interval queries. –Duplicate data is created in version split or entry reinsertion.

28. 28 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

29. 29 Strong and weak points Strong points: –Appropriate related work and good structural sequence. –Good graphic explaination method. Weak points: –No method to decide the parameters. –Does not give a solution to deal with the duplicate visit to the same node via different parents in query processing with MVR-trees.

30. 30 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

31. 31 Relation to our project Similar work to our project but different direction. MVB-tree is the extension of B-tree which we use in our project. Many ideas can be used in our project.

32. 32 Overview Motivation Related works MV3R-tree Strong and weak points Relation to our project Conclusion

33. 33 Conclusion MV3R-tree can handle both timestamp and interval queries efficiently. But update process is complex. Choose between MVR-tree and 3D R-tree is important. Duplicate can only be reduced but not be avoided.