1. Cheng, Xie, Yiu, Chen, Sun UV-diagram: a Voronoi Diagram for uncertain data 26th IEEE International Conference on Data Engineering 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)

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

3. 3Cheng, Xie, Yiu, Chen, Sun 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]

4. 4 Location Uncertainty [TDRP98,ISSD99,VLDB04]

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

6. 6 Probabilistic Nearest Neighbor Query [cheng04] INPUT 1.A query point called q 2.A set of n objects O 1,O 2,…, O n with uncertainty regions and pdfs OUTPUT A set of (O i,p i ) tuples –p i is the non-zero probability (qualification probability) that O i is the nearest neighbor of q O2O2 q f O1O1 O3O3 O4O4 O5O5 O6O6

7. 7Cheng, Xie, Yiu, Chen, Sun 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

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

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

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

11. 11 Basic Method Example: constructing U 1 Cheng, Xie, Yiu, Chen, Sun

12. 12 Basic Method O1O1 O2O2 O3O3 Example: constructing U 1 Cheng, Xie, Yiu, Chen, Sun n-1 inner region has to be constructed! Pruning techniques Evaluating Ui requires expensive numerical calculations Reference objects Candidate Reference objects

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

14. 14 Cheng, Xie, Yiu, Chen, Sun Efficient Construction Index Level Pruning Computational Level Pruning Refinement Candidate Reference Objects C i Reference Objects F i UV-index Construction Initial Possible Region Construction Possible Region P i I ndex level Pruning C omputational level Pruning R efinement I ndex level Pruning C omputational level Pruning

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

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

17. 17Cheng, Xie, Yiu, Chen, Sun Step 2,3: I- and C- Pruning O7O7 O1O1 O2O2 O3O3 O4O4 O5O5 O8O8 O6O6

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

19. 19Cheng, Xie, Yiu, Chen, Sun Experiment Setup Uncertain DatasetSynthetic: 10k – 80k (30k def) Real dataset: 17k, 30k, 36k Uncertainty pdfGaussian (represented by 20 histogram bars)

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

21. 21Cheng, Xie, Yiu, Chen, Sun Query Time’s Break-down (T q )

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

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

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

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

26. 26Cheng, Xie, Yiu, Chen, Sun 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.

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

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

29. 29Cheng, Xie, Yiu, Chen, Sun 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.