1. Join-Queries between two Spatial Datasets Indexed by a Single R*-tree Join-Queries between two Spatial Datasets Indexed by a Single R*-tree Michael Vassilakopoulos (*) (Dept. of Computer Science and Biomedical Informatics, University of Central Greece, Greece) Antonio Corral (Department of Languages and Computing, University of Almeria, Spain) Nikitas N. Karanikolas (Department of Informatics, Technological Educational Institute of Athens, Greece) (*) speaker 37th Int. Conf. on Current Trends in Theory and Practice of Computer Science, Jan. 2011, Nový Smokovec, Slovakia

2. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 2

3. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 3

4. Problem and Motivation (1)  Among the most frequent queries appearing in Spatial Databases is the Spatial Join Query: find all pairs of objects (O, O’)  R×S, where θ (O.G, O’.G) = TRUE  Examples of θ : intersects, contains, is enclosed by, distance, north-west, adjacent, meets, etc.  Usually, the intersection join is an efficient filter. 4

5. Problem and Motivation (2)  Current social and technological advancements contribute to the production of large datasets (e.g. datasets of Geographical Information Systems applications).  The size of such datasets raises the cost of join processing => the importance of the data indexing method and the query processing technique rises. 5

6. Problem and Motivation (3)  R-trees (and family) are considered good choices for indexing spatial data sets to process join queries in Spatial Databases.  When joining two datasets, a common assumption is that each dataset is indexed by a different R*-tree.  In this paper, we index both datasets by a single R*- tree, so that spatial locality between different datasets is embedded in data indexing. 6

7. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 7

8. Contribution We present  an R*-tree variation able to index two datasets (2D1T), taking advantage of the spatial locality between different datasets,  a new algorithm for processing join queries on 2D1T by Breadth-First traversal, where at each level we follow Best-First selection,  results (I/O and execution time) of comparative experimentation between 2D2T and 2D1T solutions for Intersection Join queries (on non-point datasets), K-CPQ and Buffer Queries (on point datasets). 8

9. Background  Intersection Join: discovers the pairs of objects that intersect each other. E.g. “find all trails that go through some forest”  K-CPQ: discovers the K pairs of objects that have the K smallest distances between them. It is a combination of join and nearest neighbor queries. E.g. “find the 3 closest pairs of cities and archeological sites”  Buffer Query: discovers pairs of objects that are within a threshold distance of each other. E.g. “find house-power line pairs that are within 50 meters of each other”. 9

10. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 10

11. MBRs can be recursively grouped into larger MBRs R-Tree (1) Clusters of spatial objects can be grouped into Minimum Bounding Rectangles – MBRs R1 R2 R5 R3 R7 R9 R6 R4 R8 R10R11 R12 11

12. R10 R11 R12 R1 R2 R3R4 R5 R6R7 R8 R9 Nodes that contain points R-Tree (2) Nested MBRs can be organized as a tree (R-tree) R1 R2 R5 R3 R7 R9 R6 R4 R8 R10R11 R12 The R*-tree is the most popular R-tree variation 12

13. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 13

14. 2 Datasets in 1 Tree (2D1T)  Each MBR has a dataset flag showing if it contains data related to D1 ('a'), D2 ('b'), or both ('c')  This flag does not affect the placement of data in the tree. subscript of 'a' / 'b': identifier of the element 14

15. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 15

16. Join-query Algorithms  Search algorithms (Best-First, Depth-First and Breadth-First Search) can be applied on tree-like structures for spatial queries  We have implemented all of them for all the three spatial join queries (Intersection Join, K-CPQ and Buffer Query) on 2D2T and 2D1T  In 2D1T, since the tree is only one, Self-Join variations of the algorithms are utilized  Plane-sweep is utilized to save CPU cost (it restricts the possible combinations of pairs of MBRs) 16

17. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 17

18. The New algorithm for 2D1T  We devised a Breadth-First Traversal algorithm.  It synchronously traverses the R-tree in breadth-first order, while processing the spatial predicate (join condition) one level at a time.  At each level, it creates a list with the entries that satisfy the spatial predicate, the Intermediate Candidate Entry, to be accessed at the next level.  When the leaf level is reached, two separate lists are created, one from each dataset.  Intersection plane-sweep is applied to both lists to get the final result.  Global optimization is applied level-by-level. 18

19. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 19

20. Experimental Results (1)  We used real datasets (line segments), representing roads (NArd: 569,120 segments and Grrd: 23,268 segments), railroads (NArr: 191,637 segments and rivers (Grri: 24,650 segments).  For producing point datasets, we transformed the MBRs of NArd and NArr into points.  For larger (smaller) datasets, page size was set to 4 (1) Kbytes.  Environment used: Mac BookPro, Intel Core 2 Duo, 2.4 GHz, 4 GB RAM, gcc.  Performance measurements: I/O activity (page accesses) and response time. Experimental settings 20

21. Experimental Results (2)  Results from the creation of the trees show that the 2D1T is slightly smaller, in size, than the sum of the two R*-trees that make up 2D2T (in terms of number of nodes).  E.g. for pairs of line-segment (point) datasets for NArd and NArr, the 2D1T nodes are 5393 (5490), while the sum of the 2D2T nodes are 5543 (5697). 21

22. Intersection Join Results  Algorithm for 2D2T: BFT, algorithms for 2D1T: Self-BFT and New.  New is 3.7 to 4.6 times better in I/O than BFT and 11.7 to 8.2 times worse in response time.  Self-BFT is more than 10 times worse than New algorithm in I/O and more than 3 times better than New algorithm in response time. 22

23. K-CPQ Results  Algorithm for 2D2T: Heap, algorithms for 2D1T: Self-Heap and New.  New is 3.8 times better in I/O than Heap and 2 times worse in response time.  Self-Heap is more than 3.8 times worse than New in I/O and more than 1.4 times better in response time. 23 NArd x NArr

24. Buffer Query Results  Algorithm for 2D2T: Heap, algorithms for 2D1T: Self-Heap and New.  New is 3.6 to 4.3 times better in I/O than Heap algorithm and 4.2 to 5.2 times in response time.  Self-Heap is more than 9 times worse than the New algorithm in I/O and more than 1.6 times better in response time. 24 NArd x NArr

25. LRU Buffer Effect  Intersection Join (left) by using DFT for 2D2T and by using Self-BFT and New for 2D1T.  K-CPQ (right) by using DFT for 2D2T and Self-Heap and New for 2D1T.  The I/O performance of the New algorithm was always the best and invariant to the buffer size (contrary to DFT). 25 NArd x NArr

26. Outline  Problem and Motivation  Contribution and Background  R-trees  2 Datasets in 1 Tree (2D1T)  Join-query Algorithms  The New Algorithm for 2D1T  Experimental Results (Intersection Join, K-CPQ, Buffer Query, LRU-buffer)  Conclusions and Future Work 26

27. Conclusions  We presented a tree that stores simultaneously two spatial datasets, taking advantage of spatial locality (2D1T).  We presented a New join algorithm for 2D1T.  We compared the performance of 2D2T and 2D1T for several join queries (Intersection Join, K-CPQ, Buffer Query).  2D1T exhibits a much better I/O performance, 2D2T exhibit better CPU performance.  The winner depends on the balance between CPU power and I/O efficiency of the computing system. 27

28. Future Work  To study the CPU cost of the New algorithm and focus on reducing it.  To consider 2D1T variants of structures with non- overlapping nodes, such as R + -trees, or Quadtrees, as they have been used in Y. J. Kim and J. Patel. Performance Comparison of the R*-tree and the Quadtree for kNN and Distance Join Queries. IEEE TKDE, 22(7), pp. 1014-1027, 2010.  In this paper, it is concluded that “an often dismissed index structure (the Quadtree) can be a better choice than the widely used R*-tree for index-based k-NN query and distance join algorithms when indices are constructed dynamically”. 28

29. Thank you for your attention mvasilako@ucg.gr http://users.ucg.gr/~mvasilako