1. Nearest-Neighbor Searching Under Uncertainty Wuzhou Zhang Joint work with Pankaj K. Agarwal, Alon Efrat, and Swaminathan Sankararaman. To appear in PODS 2012.

2. Nearest-Neighbor Searching Applications Pattern Recognition, Data Compression Statistical Classification, Clustering Databases, Information Retrieval Computer Vision, etc. http://en.wikipedia.org/wiki/Nearest_neighbor_search 2

3. Data Uncertainty  Location of data is imprecise: Sensor databases, face recognition, mobile data, etc. 3

4. Our Model and Problem Statement 4 0.1 0.20.30.4

5. Previous work and Our contribution 5

6. Summary of results 6 Distance function SettingsPreprocessing timeSpaceQuery time Squared Euclidean distance Uncertain data Uncertain query Rectilinear metric Uncertain data Uncertain query Uncertain data Uncertain query

7. Voronoi Diagram 7 Preprocessing time Space Query time

8. Expected Voronoi Diagram 8

9. Minimization diagram 9

10. Squared Euclidean distance Uncertain data 10 Preprocessing timeSpaceQuery time Remarks: Works for any distribution

11. Rectilinear metric Uncertain data 11

12. Rectilinear metric Uncertain data (cont.) 12 Linear!

13. Rectilinear metric Uncertain data (cont.) 13 Preprocessing timeSpaceQuery time Remarks: Extends to higher dimensions

14. 14

15. 15 Quadtree: 4-way tree Preprocessing timeSpaceQuery time

16. Further work 16

17. Squared Euclidean distance Uncertain query 17 Preprocessing timeSpaceQuery time Remarks: Extends to higher dimensions and works for any distribution

18. Rectilinear metric Uncertain query 18 Preprocessing time Space Query time

19. 19 Preprocessing time Space Query time Remarks: Extends to higher dimensions