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Continuous Intersection Joins Over Moving Objects

Continuous Intersection Joins Over Moving Objects. Rui Zhang University of Melbourne Dan Lin Purdue University Kotagiri Ramamohanarao University of Melbourne Elisa Bertino Purdue University. Outline. Backgrounds Intersection Joins on moving objects Indexes for moving objects

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Continuous Intersection Joins Over Moving Objects

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  1. Continuous Intersection Joins Over Moving Objects Rui Zhang University of Melbourne Dan Lin Purdue University Kotagiri Ramamohanarao University of Melbourne Elisa Bertino Purdue University

  2. Outline • Backgrounds • Intersection Joins on moving objects • Indexes for moving objects • Algorithms • Adapting existing algorithms • Our approach • Time constrained processing • Improvement techniques • Experiments

  3. Motivation • (Traditional) Intersection join • Given two sets of spatial objects A and B, find all object pairs ‹i,j›, where iA, j B, such that i intersects j. • Intersection join on moving objects • Moving • Continuous

  4. Join Algorithms • Nested loops join • Basic • Expensive • Block nested loops join • Efficient • Dependent on buffer size • Index nested loops join • Efficient and robust • Sort-merge join • Efficient • Difficult for spatial objects

  5. N3 N1 N3 N1 N1 N2 A D N1 N2 F C F A C D B E N2 E B Indexing Moving Objects u u u u u u • Monitoring moving objects • Sampling-based • Trajectory-based • p = p ( t ref ) + v (t - t ref ) • TM : maximum update interval • R-tree [SIGMOD’84] • Minimum bounding rectangle (MBR) • TPR-tree [SIGMOD’00] • Add time parameters to the R-tree • Other indexes: Bx-tree [VLDB’04], STRIPES [SIGMOD’04] • Only for points u

  6. Naive Algorithm (NaiveJoin) • Join nodes from two TPR-trees recursively • If intersected, check on children • Otherwise, disregard it • For an update, compute its join pairs and update the answer

  7. For the 1st TP-Join Node access (IO) roots, N1, N3 Comparison (CPU) root A vs root B, N1 vs N3 Extended TP-Join Algorithm (ETP-Join) • Time Parameterized Join (TP-Join) [SIGMOD’02] • Current result ‹a1,b1› • Expiry time 1 • Event that causes the change ‹a2,b2›

  8. Summary • ETP-Join • Cheaper traversal, but too frequent traversals • NaiveJoin • One tree traversal per update, but expensive traversal For the 1st TP-Join Too long Too short

  9. Key Problem • Find a good time range for computing the join pairs • Observation • Consider object a and b • Let the next update time for them be ta and tb • Perfect time range for computing their join result is [tc, min(ta,tb)] • How do we know ta or tb? • TM gives a bound for them • Time range is cut from [tc, ] to [tc, tc+TM] • Is this correct for all objects? • Yes. Proof in technical report: http://www.cs.mu.oz.au/~rui/publication/TR_mj.pdf

  10. Time Constrained Processing (TC-Join) • NaiveJoin with constrained processing time range [tc, tc+TM]

  11. Further Optimization (MTB-Join) • Many objects will not update at the time bound • Put objects in time buckets • Each time bucket has an associated TPR-tree • An object is inserted into the tree whose time bucket contains the object’s latest update time tc is in [TM, 3/2TM]

  12. Improvement on the Basic Join Algorithm • Plane Sweep • Sorting based on the lower left corner in dimension x • Two sequences: Sa = ‹a3, a4, a5›; Sb = ‹ b1, b2, b3, b4› • Two essential components for PS • Lower bound • Upper bound

  13. Other Improvements • Sorting dimension selection • Smaller average speed • Intersection check • First intersection check and then plane sweep

  14. Experiments: setting • Computer: 2.6G Pentium IV CPU, 1G RAM • Datasets: Uniform, Gaussian, Battlefield • Measure: IO and Time

  15. Experiments: TC processing Up to 15 times improvement

  16. Experiments: Improvement techniques Up to 6 times improvement

  17. Comparison: Initial Join MTB-Join outperforms others Half an hour for NaiveJoin

  18. Comparison: Maintenance Up to 104 times improvement

  19. Conclusion and future work • Conclusion • Time Constrained processing • Further optimization by bucketing in time • Improvement techniques • Several orders of magnitude performance improvement • Future work • Applying TC processing to other queries

  20. References • R-tree [SIGMOD’04] • Antonin Guttman. R-Trees: A Dynamic Index Structure for Spatial Searching. ACM SIGMOD Conference 1984. • TPR-tree [SIGMOD’00] • S. Saltenis, C. S.Jensen, S. T. Leutenegger, and M. A. Lopez. Indexing the positions of continuously moving objects. ACM SIGMOD Conference 2000. • Bx-tree [VLDB’04] • C. Jensen, D. Lin, and B.C.Ooi. Query and update efficient B+-tree based indexing of moving objects.International conference on Very Large Databases, 2004. • STRIPES [SIGMOD’04] • J. M. Patel, Y. Chen, and V. P. Chakka. STRIPES: An efficient index for predicted trajectories.ACM SIGMOD Conference 2004. • TP-Join [SIGMOD’02] • Y. Tao and D. Papadias. Time-parameterized queries in spatio-temporal databases.ACM SIGMOD Conference 2002.

  21. Questions Please send your questions to Rui Zhang rui@csse.unimelb.edu.au

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