UV-diagram: a Voronoi Diagram for uncertain data

1. 26th IEEE International Conference on Data Engineering UV-diagram: a Voronoi Diagram for uncertain data Reynold Cheng (University of Hong Kong) Xike Xie (University of Hong Kong) Man Lung Yiu (Hong Kong Polytechnic University) Jinchuan Chen (Renmin University of China) Liwen Sun (University of Hong Kong) Cheng, Xie, Yiu, Chen, Sun

2. Voronoi Diagram http://www.crowddynamics.co.uk/images/Personal%20Space.jpg http://www.ics.uci.edu/~eppstein/vorpic.html Cheng, Xie, Yiu, Chen, Sun

3. Voronoi Diagram • Aggregate Query in Sensor Network [Shahabi06a] • Spatial Skyline Query [Shahabi06b] • Reverse Nearest Neighbor Query [Yiu07] • Common Influence Join [Yiu08] • Uncertain Data Clustering [Kao08] Cheng, Xie, Yiu, Chen, Sun

4. Location Uncertainty [TDRP98,ISSD99,VLDB04]

5. UV-diagram(Uncertain Voronoi Diagram) (a)Voronoi Diagram. (b) UV-Diagram. Cheng, Xie, Yiu, Chen, Sun

6. Probabilistic Nearest Neighbor Query [cheng04] INPUT • A query point called q • A set of n objects O1,O2,…, On with uncertainty regions and pdfs OUTPUT • A set of (Oi,pi) tuples • piis the non-zero probability (qualification probability) that Oiis the nearest neighbor of q O5 O3 f O1 q O4 O6 O2

7. Agenda • Introduction • Basic Concepts • Voronoi Diagram in Spatial Database Management • Data Uncertainty • Applications of UV-diagram • UV-diagram • Basic concepts of UV-diagram UV-edge, UV-cell, possible region, outer region… • Construction Initial region construction, I- and C- level pruning, UV-index construction • Results • Conclusion • Future work Cheng, Xie, Yiu, Chen, Sun

8. UV-Diagram: an example UV-cell Exponential number of UV-partitions can be generated! Cheng, Xie, Yiu, Chen, Sun

9. UV-cell • We can use 3 UV-cells to represent 7 UV-partitions. • The number of UV-cells equals to the number of objects. Cheng, Xie, Yiu, Chen, Sun

10. Shape of a UV-cell Bisector Outer Region of Oi w.r.t Oj Inner Regionof Oi w.r.t Oj UV-cell is the intersection of inner regions of Oi w.r.t. all other objects Cheng, Xie, Yiu, Chen, Sun

11. Basic Method Example: constructing U1 Cheng, Xie, Yiu, Chen, Sun

12. Basic Method n-1 inner region has to be constructed! Pruning techniques O2 O1 Evaluating Ui requires expensive numerical calculations O3 Reference objects Candidate Reference objects Example: constructing U1 Cheng, Xie, Yiu, Chen, Sun

13. UV-diagram(Uncertain Voronoi Diagram) (a)Voronoi Diagram. (b) UV-Diagram. Cheng, Xie, Yiu, Chen, Sun

14. Efficient Construction Initial Possible Region Construction Possible Region Pi Index Level Pruning Index level Pruning Computational level Pruning Refinement Index level Pruning Computational level Pruning Computational Level Pruning Candidate Reference Objects Ci Refinement Reference Objects Fi UV-index Construction Cheng, Xie, Yiu, Chen, Sun

15. Step 1: Generating a Possible Region Cheng, Xie, Yiu, Chen, Sun

16. Step 1: Generating a Possible Region Cheng, Xie, Yiu, Chen, Sun

17. Step 2,3: I- and C- Pruning O7 O3 O2 O5 O8 O4 O6 O1 Cheng, Xie, Yiu, Chen, Sun

18. Splitting Condition Overlap Checking PNN Query Step 4. UV-index Construction Cheng, Xie, Yiu, Chen, Sun

19. Experiment Setup Cheng, Xie, Yiu, Chen, Sun

20. Query Performance (ms) Cheng, Xie, Yiu, Chen, Sun

21. Query Time’s Break-down (Tq) Cheng, Xie, Yiu, Chen, Sun

22. Query Performance (I/O) Cheng, Xie, Yiu, Chen, Sun

23. Construction Time Cheng, Xie, Yiu, Chen, Sun

24. Pruning Ratio Cheng, Xie, Yiu, Chen, Sun

25. Real Dataset Cheng, Xie, Yiu, Chen, Sun

26. Conclusion • We propose UV-diagram, which is a variant of Voronoi Diagram for uncertain data. • We introduce the concepts of UV-cell and reference objects to efficiently construct UV-diagram. • We also propose an adaptive index for the UV-diagram. Cheng, Xie, Yiu, Chen, Sun

27. Future Work • Use UV-diagram to support various types of queries - Continuous query, imprecise NN query, reverse NN query, etc. Cheng, Xie, Yiu, Chen, Sun

28. THANKS! Contact: Xike Xie xkxie@cs.hku.hk Department of Computer Science The University of Hong Kong 28 28 28 Q & A More discussions are welcome in the poster session!

29. Reference • [shahabi06a] Mehdi Sharifzadeh, Cyrus Shahabi: The Spatial Skyline Queries. VLDB 2006: 751-762 • [Shahabi06b] Sharifzadeh, Mehdi and Shahabi, Cyrus: Utilizing Voronoi Cells of Location Data Streams for Accurate Computation of Aggregate Functions in Sensor Networks. Geoinformatica. 2006 • [Kao08] Clustering Uncertain Data using Voronoi Diagrams: Ben Kao; Sau Dan Lee; David Cheung; Wai-Shing Ho; K. F. chan. ICDM 2008 • [Yiu07] Yiu, Man Lung and Mamoulis, Nikos. Reverse Nearest Neighbors Search in Ad Hoc Subspaces. TKDE 2007 • [Yiu08] M. L. Yiu, N. Mamoulis, and P. Karras. Common Influence Join: A Natural Join Operation for Spatial Pointsets. In ICDE 2008. • [Zheng06] B. Zheng, J. Xu, W.-C. Lee, and L. Lee, “Grid-partition index: a hybrid method for nearest-neighbor queries in wireless location-based services,” VLDB J., vol. 15, no. 1, pp. 21–39, 2006. • [cheng04] R. Cheng, D. V. Kalashnikov, and S. Prabhakar, “Querying imprecisedata in moving object environments,” TKDE, vol. 16, no. 9, 2004. • [TDRP98] P. A. Sistla, O. Wolfson, S. Chamberlain, and S. Dao,“Querying the uncertain position of moving objects,” in Temporal Databases: Research and Practice, 1998. • [ICDCS07] S. Ganguly, M. Garofalakis, R. Rastogi, and K. Sabnani, “Streaming algorithms for robust, real-time detection of ddos attacks,” in ICDCS, 2007. • [VLDB04a] A. Deshpande, C. Guestrin, S. Madden, J. Hellerstein, and W. Hong, “Model-driven data acquisition in sensor networks,” in Proc. VLDB, 2004 • [Jooyandeh09] M. Jooyandeh, A. Mohades, and M. Mirzakhah, “Uncertain voronoi diagram,” Inf. Process. Lett., vol. 109, no. 13, pp. 709–712, 2009. • [Sember08] J. Sember and W. Evans, “Guaranteed voronoi diagrams of uncertain sites,” in CCCG, 2008. Cheng, Xie, Yiu, Chen, Sun