Indexing the imprecise positions of moving objects

1. 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

3. 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, Bx-tree, Bdual-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.) * Open-source DB * Uncertainty support * DB enhancement ORION DBMS

7. 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 uncertainstationary objects.

8. 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 theclients 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 Li(p) is that the appearance probability of o on the left of Li(p) equals p • Ui(p) line segments are obtained in the same way.

17. 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

18. 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.

20. Thank you!