Efficient Algorithms to Monitor Continuous Constrained k Nearest Neighbor Queries

1. Efficient Algorithms to Monitor Continuous Constrained k Nearest Neighbor Queries Presented by: Mahady Hasan Joint work with Muhammad Aamir Cheema, Wenyu Qu, Xuemin Lin University of New South Wales, Australia

2. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

3. R o5 o5 o7 o7 o1 o3 o3 o3 q o6 o6 o2 o9 o4 o4 o4 o8 What is Constrained NN? What is NN? Finding contrained kNN objects. Let k=3 Finding kNN objects. Let k=3 Presented by: Mahady Hasan

4. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

5. Related works • Constrained kNN queries: • H. Ferhatosmanoglu et al. first introduce the constrained kNN queries (SSTD 2001). • Gao et. al find k-nearest trajectories in a constrained region. (DASFAA 2008) • Continuous k NN queries: • YPK-CNN( Yu et al. ICDE 2005) • SEA-CNN (Xiong et al. ICDE 2005) • CPM (Mouratidis et al. SIGMOD 2005) Presented by: Mahady Hasan

6. q o5 o5 o3 o8 o7 o4 o2 o5 o1 o6 Related work: CPM Heap U2 c44 U0 L0 D0 R0 c55 U1 c54 U1 c43 D0 R0 L0 c53 c55 o5 U1 L1 c53 c54 c55 U0 D0 c33 R0 c55 o5 U1 L1 D1 c34 L2 L1 L0 c43 c44 c45 R0 c35 L1 D1 R1 c45 c55 o5 U1 R2 R0 R1 c33 D0 c34 c35 D1 We check an cell or entry before we insert in the heap that it intersects with the given constrained region or not. D2 Finding one Nearest Neighbor Presented by: Mahady Hasan

7. Motivation We have observed that in case of our problem setting CPM needs to check lots of cells before it inserts the cell in the cell in the heap. So CPM becomes expensive in terms of computational time. At the same time CPM needs more space to store the heap and visit lists to update the data efficiently. So we use some other access methods that are more natural with our problem setting Presented by: Mahady Hasan

8. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

9. Concept of Grid-Tree Structure root Intermediate Entries Grid Cells Presented by: Mahady Hasan

10. o8 o4 o6 o2 o7 o8 o5 o9 o3 o1 q Grid-Tree based NN search algorithm Heap R3 c23 R2 c22 root R2 R4 R3 R1 c24 c21 c12 R2 c13 c11 c14 R4 R3 root c21 c13 c24 o8 c11 o9 c14 c22 o6 c23 R4 R3 R4 c13 R1 c12 c14 c11 Presented by: Mahady Hasan

11. R o1 o3 o4 o5 o6 o7 o2 o7 o8 o1 o5 o8 o2 root q Grid-Tree Based constrained NN Algorithm Heap R3 c33 c32 R2 R4 R3 c34 c31 c43 c42 R3 root c31 c32 c34 c33 c43 R4 c43 c42 R1 c32 o2 c43 c34 c33 o4 c32 o2 c43 c34 c33 c44 c41 Presented by: Mahady Hasan

12. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

13. θend r θstart cstart q Concept of ArcTrip • Input: • Radius r • Angle rangeθstart ,θend c41 c42 c43 c44 r θstart θend c31 c32 c33 c34 • Output: • cells that intersect the arc with in θstart and θend • with radius r from the query point q c21 c22 c23 c24 c11 c12 c13 c14 Returned values are c22, c32, c33 Presented by: Mahady Hasan

14. θend q.cNNdist r o3 o9 o1 o3 o3 o5 o2 o6 o4 o5 o7 θstart q ArcTrip Based contained NN Algorithm Heap c41 c42 c43 c42 c22 c32 c31 c32 c33 cNN o3 o5 c21 c22 c24 c11 c12 c13 c14 Finding 1 constrained NN Presented by: Mahady Hasan

15. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

16. Continuous monitoring • Phase 1: receive object and query updates. • Find affected queries. • Change in the queries based on the update below. • Internal update (dist(oold,q)≤q.distkΛ dist(onew,q)≤q.distk) • Arrange the order in q.CkNN • Incoming update (dist(oold,q)>q.distkΛ dist(onew,q)<q.distk) • Insert object in q.CkNN • Outgoing update (dist(oold,q)≤q.distkΛ dist(onew,q)>q.distk) • Remove object from q.CkNN Presented by: Mahady Hasan

17. Continuous monitoring … • Phase 2: Check the status of each query one by one • If query moved then • Execute the initial algorithm. • If q.CkNN > k then • Keep top k objects and remove rest of the objects. • If q.CkNN < k then • Expand the search area by visiting more cells Presented by: Mahady Hasan

18. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

19. Experiment Setup Brinkhoff data generator; Oldenburg city (Germany). Presented by: Mahady Hasan

20. Grid cardinality effect Need to check many empty cells. Need to check too many objects. Presented by: Mahady Hasan

21. Grid Memory Effect CPM stores the heap and the visit list. Presented by: Mahady Hasan

22. Effect of k size Presented by: Mahady Hasan

23. Cardinality Effect Updating in CPM become expensive Presented by: Mahady Hasan

24. Speed Effect In CPM paper it was showed that speed has no affect. Presented by: Mahady Hasan

25. Agility effect With increase in query agility CPM needs to compute the results from the scratch. Object agility results more updates so the computation cost increases. Presented by: Mahady Hasan

26. Outline of the Presentation • Introduction • Related Work (Motivation) • GridTree Approach • ArcTrip Approach • Continuous monitoring • Experiments • Conclusion Presented by: Mahady Hasan

27. Conclusion • We proposed two novel Grid access methods. • We devise two algorithms to compute the constrained k nearest neighbors. • Our experimental results show our algorithms performs much better than the existing algorithm in terms of memory space and run time. Presented by: Mahady Hasan

28. Thank you… Questions??

29. R Cell 2 Cell 1 maxdist(q,Cell2) mindist(q,Cell1) maxcdist(q, Cell2) mincdist(q, Cell1) q Some changes to calculate distance Presented by: Mahady Hasan