Indexing the imprecise positions of moving objects Xiaofeng Ding and Yansheng Lu Department of Computer Science Huazhong University of Science & Technology Wuhan, China.

2 Outline of the Talk  Background  The moving objects with uncertainty  Query evaluation and indexing  Conclusions

Application pull  Many applications need to manage imprecise data Scientific applications Global Positioning System Sensor databases Meteorology system Location based services  The reasons bring imprecision Measurement error Sampling error Update delay Etc..

4 Technology push  Indexing methods R-tree, MVR-tree, HR-tree, … TPR-tree, TPR*-tree, B x -tree, B dual -trees …  Range search R-tree, MVR-tree, HR-tree,  Nearest neighbor Time parameterized NN Continuous NN Location based NN  Reverse nearest neighbor  Stream processing  …

5 Technology push (Cont.)  Orion DBMS  TRIO project  ConQuer project  U-tree All the above work assumes that the database has the exact location of each object. But this is rarely possible.

6 Technology push (Cont.) ORION DBMS * Open-source DB * Uncertainty support * DB enhancement * Uncertainty support * DB enhancement

Technology push (Cont.)  Uncertain range search [Reynold et al. VLDB 04], [Tao et al. VLDB 05]  Uncertain nearest neighbor search [Reynold et al. SIGMOD 03, TKDE 04]  Uncertain join processing [Reynold et al. CIKM 06] All existing work considers only uncertain stationary objects.

Uncertain model of moving objects The moving object’s location is described by a probability density function within the uncertainty region.

9 Constrained imprecise range query Find the clients that are currently in the town center with at least 50% appearance probability.

10 Qualification probability Qualification probability : Calculation time of an appearance probability in 2D space: 1.3ms Time for a random I/O access: 10ms

11 Goal  Support any pdf  Minimize the number of page accesses  Minimize the number of qualification probability calculations.  Minimize the total cost (I/O + CPU)

12 Main idea  For each moving object, pre-compute the velocity constrained region (VCR) to: Instead the uncertainty region  Uncertainty region is usually a polygon  VCR is usually a rectangle Efficiently calculate whether an object appears in a query region with at lest a certain probability  The pdf within VCR is known as Uniform or otherwise

13 Quick examples VCR:

14 Quick examples (cont.) Suppose the probability density function pdfi(x, t) of VCRi(t) is a bounded uniform distribution: pdfi(x, t) = If the imprecise range query is evaluated at time t, then the qualification probability will be:

15 p-bound  Pre-compute some “ auxiliary information ” that can be used to efficiently decide whether an object appears in a region with at least a certain probability without calculating its actual appearance probability. p-bound of a d-dimensional moving object:

16 Quick examples  The p-bound of an uncertain moving object o takes a parameter p whose value is between [0, 0.5]: The requirement of L i (p) is that the appearance probability of o on the left of L i (p) equals p U i (p) line segments are obtained in the same way.

Indexing  Indexing is necessary Query time is affected by the number of objects that to be considered For a large collection of points, it is impractical to evaluate each point to answer the query.  Indexing the moving object with uncertainty in the virtue of TPR*-tree Velocity constrained index

Other issues  Calculation optimization  Nearest neighbor queries  Reverse nearest neighbor queries  Join processing  Metircs for measuring the answer quality

19 Conclusions  Notions about uncertain moving objects Uncertain models Kinds of queries.  The effective method for answering constrained imprecise range queries Pre-computed velocity constrained region The concept of p-bound Indexing methods.

Thank you!