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

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

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

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

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

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

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

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

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

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

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.