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Close Pair Queries in Moving Object Databases

This presentation addresses the Close Pair Query within moving object databases, which involves identifying pairs of objects that are within a specified distance in a defined time and space range. It covers the problem definition, the motivation behind the study (including real-world applications like detecting accidents), and the proposed algorithm. Key components include the Retrieval and Identification components using the MTSB-tree structure. Experimental results and conclusions will also be discussed, highlighting the challenges and solutions in efficiently querying moving object data.

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Close Pair Queries in Moving Object Databases

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  1. Close Pair Queries in Moving Object Databases Panfeng Zhou, Donghui Zhang, Betty Salzberg, Gene Cooperman Northeastern University George Kollios Boston University

  2. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  3. Problem definition • Example: Which airplanes were closer to each other than 10 miles during the past month in Massachusetts? • Formal definition: Given a trajectory dataset D, a spatial range R, a time interval I and a threshold ε, the Close-Pair Query finds all pairs of object IDs (o1, o2) such that at some time t Є I, o1 and o2 are both located inside R and d(o1, o2) < ε.

  4. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  5. Motivations • Close pair query can be used to find associations and correlations between objects (e.g., S. Shekhar and Y. Huang, “Discovering Spatial Co-location Patterns: A Summary of Results”, SSTD 2001). • Close pair query itself can be used in many real applications.

  6. ACCIDENTS Motivations (cont) INCIDENTS UNREPORTED OCCURRENCES Heinrich Pyramid

  7. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  8. Algorithm • Overview Structure • Retrieval component • Identification component

  9. Identification Component (Time-X Plane Sweep) Retrieval Component (MTSB-tree) Overview structure of algorithm Close pairs Trajectories in increasing time order

  10. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  11. Retrieval component • Overview of the MTSB-tree • Challenges in the MTSB-tree • How to avoid sorting • How to avoid duplication

  12. TSB-tree 2 TSB-tree 1 TSB-tree 3 TSB-tree 5 TSB-tree 4 TSB-tree 6 TSB-tree 8 TSB-tree 7 TSB-tree 9 Overview of the MTSB-tree • Note: • Trajectory covers multi- cells will be saved in all those cells. • The retrieval algorithm will first find all the cells intersect spatial range R. Within each cell, load all the pages intersect time range I.

  13. Challenges in the MTSB-tree • Output the retrieval results in time increasing order. • Avoid loading the same trajectory multiple times.

  14. How to avoid sorting - 1 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 Cell 1 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  15. How to avoid sorting - 2 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 T1, L11 Cell 1 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  16. How to avoid sorting - 3 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 T1, L11 Cell 1 T2, L21 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  17. How to avoid sorting - 4 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 T1, L12 Cell 1 T2, L21 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  18. How to avoid sorting - 5 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 T2, L21 Cell 1 T5, L13 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  19. How to avoid sorting - 6 Page 1 Page 2 Priority Queue T1, L12 T7, L14 T1, L11 T5, L13 Cell 1 T4, L22 Cell 1 T5, L13 Cell 2 Page 1 Page 2 T4, L22 T8, L24 T2, L21 T6, L23 Cell 2

  20. X Query time interval Cell 2 Spatial query range Cell 1 QET Time How to avoid duplication loading from different cells

  21. X Query time interval Spatial query range QET Page 2 Page 1 Time How to avoid duplication loading from the same cell

  22. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  23. Identification component • Motivation for TIME-X sweep algorithm • Observations • Algorithm

  24. X X ε ε ε Time Time Motivation

  25. Observations • Only need to detect close pairs at start times, end times and intersections • If two trajectory segments do not intersect, • they are closest at the start/end time of one of them • Store trajectories relative positions in X-dimension at their start times and update the order at intersections, we can always keep the correct relative order • If two trajectory segments do not intersect, • their relative positions will never change • If two trajectory segments’ distance at X-dimension • is bigger than ε, their distance at X-Y plane is also • bigger than ε • Plane sweep at TIME-X plane can filter out the unqualified close pair candidates in TIME-X-Y plane.

  26. t1: X L1 SL: EL: t8, L1 ends L1 t1 t8 Time Algorithm - 1

  27. t3: L2 SL: L1 L2 EL: t8, L1 ends t12, L2 ends t3 t12 Algorithm - 2 X L1 t1 t8 Time

  28. t5: L2 SL: L3 L1 L3 EL: t8, L1 ends t11, L3 ends t12, L2 ends t5 t11 Algorithm - 3 X L2 L1 t1 t3 t8 t12 Time

  29. t7: SL: L2 L3 L1 L4 EL: t8, L1 ends t10, L4 ends L4 t11, L3 ends t12, L2 ends t7 t10 Algorithm - 4 X L2 L3 L1 t1 t3 t5 t8 t11 t12 Time

  30. t8: Close pair candidates: (L1,L3), (L1,L4) SL: L2 L3 L4 ε ε EL: L1 t10, L4 ends t11, L3 ends t1 t8 t12, L2 ends Algorithm - 5 X L2 L3 L4 t3 t5 t7 t10 t11 t12 Time

  31. t10: Close pair candidates: (L1,L3), (L1,L4) SL: L2 L3 L4 EL: t11, L3 ends t12, L2 ends t7 t10 Algorithm - 6 X L2 L3 t3 t5 t11 t12 Time

  32. t11: Close pair candidates: (L1,L3), (L1,L4) SL: L2 L3 EL: t12, L2 ends t5 t11 Algorithm - 7 X L2 t3 t12 Time

  33. t12: Close pair candidates: (L1,L3), (L1,L4) SL: L2 EL: t3 t12 Algorithm - 8 X Time

  34. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  35. Experimental results • Setup • Retrieval component • Identification component

  36. Setup • Simulated Air Traffic Control data set includes 200,000 3-D line segments and the whole space is a 10000x10000x10 space. • 4D R*-tree (i.e., 3D for spatial, 1D for temporal) uses the XXL library • Page size: 16KB

  37. Retrieval component - 1

  38. Retrieval component - 2

  39. Identification component

  40. Talk Outline • Problem description • Motivation • Algorithm • Overview structure • Retrieval component • Identification component • Experimental results • Conclusions

  41. Conclusions • The MTSB-tree can efficiently return the retrieval results without sorting. • The Time-X plane sweep algorithm can avoid the unnecessary comparisons. • The efficiency of the methods are verified by extensive experimental results.

  42. Thank you!

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