1. Scalable Network Distance Browsing in Spatial Database Samet, H., Sankaranarayanan, J., and Alborzi H. Proceedings of the 2008 ACM SIGMOD international Conference on Management of Data Presented by: Don Eagan Chintan Patel http://www-users.cs.umn.edu/~cpatel/8715.html

2. Outline Motivation Problem Statement Proposed Approach Other Approaches Evaluation Our Comments Questions

3. Motivation Growing Popularity of Online Mapping Services

4. Motivation Real Time Shortest Paths

5. Motivation Static Network, Variable Queries Find Gas Stations, Hotels, Markets etc.

6. Motivation Static Network, Variable Queries Find Gas Stations, Hotels, Markets etc.

7. Problem Statement Input: Spatial Network S, Node q from S Output: k-nearest neighbors of q Objective: Facilitate “fast” shortest path queries based on different search criteria's Constraints/ Assumptions: Static spatial network Contiguous (connected) regions

8. Challenges Real-time response Calculating all pairs shortest path is costly Storing pre-computed naïvely doesn’t solve the problem Scalability

9. Contribution Efficient path encoding Efficient retrieval Abstracting shortest path calculation from domain queries

10. Key Concepts Spatial Networks Nearest Network Neighbor Quad Tree Morton Blocks Decoupling Scalability Pre-computing

11. Spatial Networks Graph with spatial components represented as nodes/ edges Most Transportations are modeled as graph Intersection – Node/ vertex Roads – Edge Time/ Distance – Edge Weight

12. K-Nearest Neighbors

18. Shortest Path Dijkstra’s algorithm Doesn’t work for real-time queries Computationally expensive

19. Proposed Approach Pre-compute shortest paths Store and Retrieve Efficiently N = Number of vertices, M = Number of edges, s = Length of the shortest path MethodSpaceRetrieval Time ExplicitO(N^3)O(1) DijkstraO(N + M)O(M + N log N) SLIC O(N √N ) O(s log N)

20. Path Encoding Path coherence Vertices in close proximity share portion of the shortest paths to them from distant sources

21. Path Encoding Path coherence Vertices in close proximity share portion of the shortest paths to them from distant sources

22. Path Encoding Path coherence Vertices in close proximity share portion of the shortest paths to them from distant sources

23. Path Encoding Path coherence Vertices in close proximity share portion of the shortest paths to them from distant sources

24. Path Encoding Quadtree: Decompose until all vertices in block have same color

25. How is space reduced? Capturing boundaries !

26. Path Retrieval Retrieve quadtree corresponding to s

27. Path Retrieval Find connected node t in the quadtree containing d

28. Path Retrieval Repeat the process

29. K-nearest Neighbor Set of objects Pre-computed paths (quadtree)

30. K-nearest Neighbor K = 2

31. K-nearest Neighbor Queue1: m a b Queue2: a b

32. K-nearest Neighbor Queue1: a g e b f Queue2: a g

33. K-nearest Neighbor Queue1: a g e Queue2: a g

34. K-nearest Neighbor Return a and g

35. Other Approaches IER: Incremental Euclidian Restriction Based on Euclidian distance Dijkstra’s algorithm to get network distance INE: Incremental. Network Expansion Dijkstra's algorithm with a buffer L containing the k nearest neighbors seen so far in terms of network distance

36. Evaluation Micro benchmark Synthetic Data

37. Evaluation Real Data Set: Major Road of the USA

38. Our Comments We Liked: Decoupling shortest path and neighbor calculation Space reduction approach Scalable Correctness proofs Detailed discussion about KNN variants

39. Our Comments What we didn’t like: Experiments: No comparison with other approaches (e.g. hierarchical, dynamic etc.) No performance graphs/ discussion with real dataset

40. Discussion Other use cases? Real Application: How to overcome assumptions?

41. Questions ? ? ?