Continuous Reverse Nearest Neighbor Monitoring

1. Continuous Reverse Nearest Neighbor Monitoring Tian Xia, Donghui Zhang College of Computer and Information Science Northeastern University ICDE 2006, Atlanta, GA

2. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

3. Static NN and RNN Query • Nearest Neighbor (NN) Query: Given a set of objects O and a query point q, determine the object closest to Q. q o1 ICDE 2006, Atlanta, GA

4. Static NN and RNN Query • Reverse Nearest Neighbor (RNN) Query: Given a set of objects O and a query point q, determine the objects which have Q as their nearest neighbor. o2 o4 q o1 o3 ICDE 2006, Atlanta, GA

5. Continuous Queries • In moving-object databases, the query results are constantly changing over time. • Continuous queries is to monitor the correct query results over time. • Motivating examples are the numerous location-based applications: traffic monitoring, enhance 911 service, mixed-reality games, and etc. ICDE 2006, Atlanta, GA

6. Our Problem • Continuous Reverse Nearest Neighbor (CRNN) Query: Given a set of objects O and a set of query points Q, all being static or moving, monitor the exact reverse nearest neighbors of each query point over time. ICDE 2006, Atlanta, GA

7. Time stamp 2 o2 o4 q o1 o3 CRNN Query: Example Time stamp 1 o2 o4 q o1 o3 Results: o3 and o4. Results: o1, o3 and o4. ICDE 2006, Atlanta, GA

8. Problem Setup • Objects and query points are moving unpredictably. Objects send their location updates to the server. • Objects and query points are indexed using a regular grid to ensure short location-update time. ICDE 2006, Atlanta, GA

9. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

10. q Solutions to static RNN Query • Pre-computation based solutions (Korn and Muthukrishnan, 2000; Yang and Lin, 2001). o4 o3 ICDE 2006, Atlanta, GA

11. q Solutions to static RNN Query • SAE approach (Stanoi, et al., 2000) 60o 60o ICDE 2006, Atlanta, GA

12. Solutions to static RNN Query • TPL approach (Tao, et al., 2004) o4 q o1 o3 ICDE 2006, Atlanta, GA

13. Straightforward solution for CRNN • To answer continuous RNN query, repeatedly re-compute from scratch the reverse nearest neighbors of every query point, upon every update. • Lots of computations are wasted! ICDE 2006, Atlanta, GA

14. Incremental Result Update • Continuous range query (q1 and q2) and continuous NN query (q3). q1 q3 q2 • Shadowed area is called the monitoring region. • Updates outside the monitoring region will not affect the results. ICDE 2006, Atlanta, GA

15. Why CRNN query is difficult? • Compared to static RNN query, incremental update and computation of query results are required. • Compared to other continuous queries, CRNN query has no simple monitoring regions, due to the complex nature of the RNN query. ICDE 2006, Atlanta, GA

16. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

17. Three properties of a simple monitoring region • Has a simple and regular shape. • Contains only the result objects. • Only rely on the distance between query and object. Continuous range query o2 q o1 Continuous NN query ICDE 2006, Atlanta, GA

18. o2 The Monitoring Regions of the CRNN Query • The monitoring region of a CRNN query point does not satisfy any of the three properties. o4 q o1 o3 ICDE 2006, Atlanta, GA

19. S5 S4 S0 S1 S3 S2 The Monitoring Regions of the CRNN Query • The monitoring region of a CRNN query point consists of two parts: pie-regions (shadowed) and circ-regions (red circles). ICDE 2006, Atlanta, GA

20. The Monitoring Regions of the CRNN Query • Pie-regions monitors all possible candidates (at most six). • Updates in the pie-regions may change the candidate set. • Circ-regions decides whether a candidate is a false positive or not. • Updates in the circ-regions may invalidate positive candidates, or vice verse. • The two kinds of regions are stored and manipulated completely differently! ICDE 2006, Atlanta, GA

21. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Initialization • Incremental Monitoring • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

22. Initializing CRNN Query • Combining SAE and Conceptual Partitioning (Mouratidis, et al. 2005). Features: • Performing six constrained NN searches simultaneously and optimally. • Partially integrating the refinement step with the filter step, due to the relaxation of the circ-regions. ICDE 2006, Atlanta, GA

23. Initializing CRNN Query S5 • Early invalidation of candidate (e.g. o2) is done as much as possible in the filter step, saving NN search in the refinement step. c3,6 S0 S4 q c3,5 o1 o3 o4 o2 S1 S3 S2 c0,0 ICDE 2006, Atlanta, GA

24. Storing the Pie-regions • The pie-regions are stored using the book-keeping technique, i.e. by associating cells and query points together. • Each query point stores up-to six candidates and the distances to them. ICDE 2006, Atlanta, GA

25. Updating the Pie-regions Three cases: • Some object enters a pie-region which does not contain it. • A candidate leaves its pie-region. • A candidate moves within its pie-region. • Pie-regions are expanded (shrunk) by associating (un-associating) the new (old) cells. • In all three cases, the corresponding circ-regions need to be updated. ICDE 2006, Atlanta, GA

26. Why treat the circ-regions differently? • A circ-region may change frequently, even if the corresponding pie-region is unchanged. • Circ-regions is not always changed incrementally. • Computation of NN queries for candidates is expensive and not always necessary. • Circ-regions do not need to be kept tight all the time! ICDE 2006, Atlanta, GA

27. Storing the Circ-regions • The candidates of all query points are indexed by an in-memory Frequently Update R-tree (FUR-tree. Lee, et al., 2003). • Circles are virtually stored in the FUR-tree, i.e. the FUR-tree is augmented by the radiuses of circ-regions. • Objects invalidating the candidates are stored in a separate hash table (called “NN-Hash”), with pointers to the corresponding candidates. o8 FUR-tree Internal Hash table pointing to each leaf object o6 o2 o1 ~ o6 o5 o1 o4 NN-Hash o3 o2 o7 o1 o8 o7 ICDE 2006, Atlanta, GA

28. o6 Updating the Circ-regions: the Lazy-Update Optimization • Candidates are updated efficiently! • Most of the NN search are avoided! o7 o8 o6 o8 o8 o7 o6 ICDE 2006, Atlanta, GA

29. Partial-Insert Optimization • Only large circ-regions are stored in the FUR-tree. • Rationale: small circ-regions are unlikely to cause any result update, thus are stored separately in a hash table. Benefits: • FUR-tree size is reduced, leading to more efficient query processing. • There are less number of circ-region updates. • Insertion of a small circ-region is very simple. ICDE 2006, Atlanta, GA

30. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

31. Experimental Settings • Dataset: Network based Generator of Moving Objects (Brinkhoff, 2002). • # of objects (K): 10, 20, 40, 60, 80, 100 • # of query points (K): 1, 2, 4, 6, 8, 10 • Object mobility (%): 1, 5, 10, 15, 20 • Query point mobility (%): 1, 5, 10, 15, 20 ICDE 2006, Atlanta, GA

32. Comparison with TPL • TPL-FUR: straightforwardly apply static TPL method on FUR-tree. • Incremental: our complete incremental approach. ICDE 2006, Atlanta, GA

33. Effects of Optimizations (1) • Uniform: store and manipulating pie- and circ-regions uniformly. • LU-only: apply Lazy-Update optimization only. • LU+PI: apply both Lazy-Update and Partial-Insert optimizations. ICDE 2006, Atlanta, GA

34. Effects of Optimizations (2) • Uniform: store and manipulating pie- and circ-regions uniformly. • LU-only: apply Lazy-Update optimization only. • LU+PI: apply both Lazy-Update and Partial-Insert optimizations. ICDE 2006, Atlanta, GA

35. Outline • Background and Definitions • Related Work • The Monitoring Region • Query Processing • Experimental Results • Conclusions ICDE 2006, Atlanta, GA

36. Conclusions • We addressed an interesting problem of monitoring continuous reverse nearest neighbors (CRNN) in a dynamic environment. • We defined an effective monitoring region of a CRNN query point. • We presented an incremental and scalable approach, and two important optimizations. • Our experiments showed our method is much more efficient than straightforward ones. ICDE 2006, Atlanta, GA

37. THANK YOU! QUESTIONS? ICDE 2006, Atlanta, GA