1. Uncertain Data Mobile Group 报告人：郝兴

2. Paper List • Querying Imprecise Data in Moving Object Environments. [TKDE 2004] Reynold Cheng, Dmitri V. Kalashnikov, and Sunil Prabhakar. • Indexing Multi-Dimensional Uncertain Data with Arbitrary Probability Density Functions. [VLDB 2005 ] Yufei Tao, Reynold Cheng, Xiaokui Xiao, Wang Kay Ngai, Ben Kao, Sunil Prabhakar. • Efficient Evaluation of Imprecise Location-Dependent Queries. [ICDE 2007] Jinchuan Chen, Reynold Cheng • Preserving User Location Privacy in Mobile Data Management Infrastructures. [PET 2006] Reynold Cheng, Yu Zhang, Elisa Bertino, and Sunil Prabhakar. • Probabilistic Spatial Queries on Existentially Uncertain Data. [SSTD 2005] Xiangyuan Dai, Man Lung Yiu, Nikos Mamoulis, Yufei Tao, and Michail Vaitis. • Probabilistic Skylines on Uncertain Data. [VLDB 2007] Jian Pei, Bin Jiang, Xuemin Lin, Yidong Yuan

3. Efficient Evaluation of Imprecise Location-Dependent Queries Jinchuan Chen Reynold Cheng Department of Computing The Hong Kong Polytechnic University

4. Outline • A Classification of ILDQ • 3 methods: • The Minkowski Sum • Query-Data Duality • Exploiting Probability Threshold

5. IPQ and IUQ A A q Point object R Uncertainty of Query issuer Uncertain object IPQ: Imprecise Location-Dependent Queries over Point Objects IUQ: Imprecise Location-Dependent Queries over Uncertain Objects

6. Method 1: The Minkowski Sum A U R B

7. w h R R Method 2: Query-Data Duality Point Object Query Point w h R Query Point Point Object

8. Query-Data Duality and IPQ A Uncertainty of Query Issuer U

9. Method 3: Probability Threshold A p-expanded-query U R R Ф U

10. The p-bound [VLDB04] p p p Uncertainty region 0  p  0.5 p

11. e e d d Deriving p-expanded-querywith p-bound p-bound (top) p-expanded-query U R Ф U p-bound (left)

12. A Pruning Uncertain Objects for C-IUQ (1) • Strategy 1: Use p-bound Uncertain object U p-bound R Ф U

13. A Pruning Uncertain Objects for C-IUQ (2) • Strategy 2: Use p-expanded query p-expanded-query U R Ф U

14. y-expanded-query Qp-expanded-query Pruning Uncertain Objects for C-IUQ (3) • Strategy 3: Use both p-bound and p-expanded query If x  y < p, then A can be pruned. A U R Ф U x-bound Qp-bound

15. Probabilistic Spatial Queries on Existentially Uncertain Data Xiangyuan Dai (HKU), Man Lung Yiu (HKU),Nikos Mamoulis (HKU) Yufei Tao (CityU,HK) Michail Vaitis (U Aegean, GR)

16. Outline • Introduction • Definitions • Evaluation of Probabilistic Queries - range queries - nearest neighbor queries

17. Introduction

18. Definitions • We refer to Ex as existential probability or confidence of x. • We identify two types of probabilistic spatial queries on existentially uncertain objects. - Thresholding query - Ranking query

19. Evaluation of Probabilistic Queries • range queries • 􀂾A depth-first search algorithm applied on the R-tree to retrieve the qualified objects • 􀂾Let Px = Ex • 􀂾Thresholding query: t is used to filter out objects with Px<t • 􀂾Ranking query: a priority queue maintains the m results with the highest Px

20. Evaluation of Probabilistic Queries • nearest neighbor queries Pm = 0 • Pfirst = 1 • p7:Px=0.1 [not a result] Pfirst=1-0.1=0.9 • p8:Px=0.9*0.2 = 0.18 [not a result] Pfirst = 0.9*(1-0.2)=0.72 • p6:Px=0.72 x 0.1 = 0.072 [not a result] Pfirst = 0.72*(1-0.1)=0.648 • p4,:Px=0.648 x 0.5 = 0.342 [result !!!] Pfirst = 0.648*(1-0.5)=0.342 • p5:Px=0.342 x 0.9 = 0.308 [result !!!] Pfirst = 0.342*(1-0.9)=0.034 • Since Pfirst = 0.034 < t= 0.3, the algorithm terminates! Pm

21. Probabilistic Skylines on Uncertain Data Jian Pei Simon Fraser University, Canada Bin Jiang, Xuemin Lin, Yidong Yuan The University of New South Wales & NICTA, Australia

22. Outline • Introduction • Probabilistic Skyline Computation • Bounding-Pruning-Refining • Bottom-Up Method • Top-Down Method

23. Introduction ——Conventional Skylines • n-dimensional numeric space D = (D1, …, Dn) • Large values are preferable • Two points, u dominates v (u ≻ v), if • " Di (1 ≤ i ≤ n), u.Di ≥ v.Di • $ Dj (1 ≤ j ≤ n), u.Dj > v.Dj • Given a set of points S, skyline = {u | uÎS and u is not dominated by any other point} • Example • C ≻ B, C ≻ D • skyline = {A, C, E}

24. Introduction ——Skylines on Uncertain Data • Example • A set of object S = {A, B, C} • Each instance takes equal probability (0.5) to appear • Probabilistic Dominance • Pr(A ≻ C) = 3/4 • Pr(B ≻ C) = 1/2 • Pr((A ≻ C) ∨ (B ≻ C)) = 1 • Pr(C is in the skyline) ≠ (1 - Pr(A ≻ C)) × (1 - Pr(B ≻ C)) • Probabilistic dominance ≠≻ Probabilistic skyline

25. Probabilistic Skyline Computation • Bottom-Up Method • " u at layer-k, $ u′at layer-(k-1), s.t., u′≻ u and Pr(u′) ³ Pr(u) • max{Pr(u) | u is at layer-(k-1)} ³ max{Pr(u) | u is at layer-k}

26. Probabilistic Skyline Computation • Top-Down Method • Partition Tree • Bounding with Partition Trees

27. Thank you Thank you