Uncertain Data Mobile Group 报告人：郝兴

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

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

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

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

Method 1: The Minkowski Sum A U 利用Minkowski Sum找到最大的基于不确定区域U的最大查询框，然后利用这个最大的查询框来做pruning R B

Method 2: Query-Data Duality Point Point Object R w h R w h R Intuition: The role of query issuer and the point objects can be exchanged Lead to simpler evaluation of IPQ and IUQ Query Point Point Object

Query-Data Duality and IPQ Uncertainty of Query Issuer U Query at the point object! Enables simpler probability evaluation

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

The p-bound [VLDB04] p p-bound 0.1 0.3 0.5 p p p Uncertainty region The p-bounds shrink with increasing value of p. In practice, a few p-bounds are pre-computed and stored p

Deriving p-expanded-query with p-bound p-bound (top) d d U p-expanded-query R Ф U p-bound (left)

Pruning Uncertain Objects for C-IUQ (1) Strategy 1: Use p-bound A Uncertain object U The concept of p-bound and p-expanded-query can also be used for C-IUQ. We have developed 3 strategies. The first one uses the p-bound, 2nd one uses p-expanded query, and the 3rd one uses both. Their details can be found in our paper. p-bound R Ф U

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

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

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)

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

Introduction

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

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

Evaluation of Probabilistic Queries nearest neighbor queries 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 = 0 Pm

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

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

——Conventional Skylines 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}

——Skylines on Uncertain Data 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

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}

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

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