1. Group 8: Denial Hess, Yun Zhang Project presentation

2. Messages What :Get near real-time K nearest neighbor (KNN) query responses in spatial networks, while minimizing the storage cost How: 1) Calculate shortest path: Dijkstra-based approach  Pre-compute –based approach 2) Search query objects: Blind search  Hierarchical algorithm to skip regions where no query object type is contained Evidence: location-based service

3. Agenda Motivation Notation Problem Statement Related Work Proposed Solution Validation Summary

4. Motivation Popularity of query in spatial networks Online map service Mobile service KNN query is basic and widely used Existing approach Can work out KNN query answer But, for typical spatial network (100,000 nodes, 100,000 edges) -> expensive computational cost or storage cost Therefore: Need more effective algorithm!

5. Notation (1/2) Graph G= (N, E, C): a directed flat graph consisting of a node set N, a cost set C, and an edge set E. Fragment: a sub-graph of G, which consists a subset of nodes and edges of G. Boundary node (BN): a node that has neighbors in more than one fragment. Hierarchical graph: a 2-level representation of the original graph. The lower-level is composed of a set of disjoint fragments The higher-level is comprised of the boundary nodes

6. Notation (2/2) Materialization: Full: all relevant information pre-computed and stored. Virtual: no information pre-stored. Hybrid: some relevant information pre-stored, some left for real-time computation.

7. Problem Statement Research question: how can we get a near real time response to KNN query in a spatial network, while minimizing the storage cost? Given: Graph G, a query node q, a required number of nearest neighbors k. Output: k nearest neighbors of query node q. Objective: near real time query response, minimize storage cost Constraint: output is correct. Computation is based on spatial network. Spatial network is static.

8. Related Work Solution-based approach (store distances between all pairs of nodes) limitation: storage cost Dijkstra-based approach (Dijkstra algorithm) limitation: computational cost Pre-compute-based approach (reduce search regions) limitation: storage cost Pre-knowledge-based approach (assume query object type is known in advance) limitation: assumption is not practical

9. Proposed Solution 1) To speed up shortest path calculation  Pre-compute 2) To avoid blind search in spatial networks  Hierarchical algorithm to skip regions where no query objects are contained

10. Challenges Need to decide a proper degree of materialization Need to deal with situations like: Large spatial network data; Query node is moving; These situations cause computational and storage challenges.

11. Working Steps a) Use CCAM to represent spatial network (involve graph partition, build hierarchy) b) Pre-compute and store shortest path information c) Use ‘Incremental Network Expansion’ framework; Use pre-compute results to calculate shortest paths ; Use hierarchy to skip regions;

12. Solution Example (1/2) Spatial Network Graph Node = object, Edge = Street Digital number=distance yellow node=query node Figure 1: Shortest path calculation

13. Solution Example (2/2) q q n1 n2 n3 n5 n4 n7 n6 Figure 2: Skip regions which contain no query object type

14. Validation (1/3) Comparison of materialization SPC-B: store shortest path cost between boundary nodes; SPC-B,IB: store shortest path cost between boundary nodes and shortest path cost between interior nodes and boundary nodes; Test Data : A real road network CA (10,000 nodes, 10,215 edges)

15. Validation (2/3) Performance Measure Storage Size; Execution Time;

16. Validation (3/3) ApproachStorage Cost Complexity IERO(N) INEO(N) Shortest Path Quadtree H-KNN O(N^ 1.5) O(N^ 1.33) N is the total nodes of a spatial network

17. Moving Object a a b b e e f f c c d d q q q is a moving object Shortest path cost from q to c: Min{ |qa|+|ac|, |qb|+|bc|}

18. Network Update a a b b c c d d Edge value |bc| increase Original shortest path from a to d: a b c d Store shortest path information: Address network update: 1)Detect affected shortest paths 2)Update shortest paths, shortest paths cost Edge value |bc| decrease Original shortest path from a to d: a d

19. Summary Contribution: Get near real-time K nearest neighbor (KNN) query responses in spatial networks, while minimizing the storage cost Novelty: 1) Speed up shortest path calculation: Pre-compute –based approach 2) Speed up query objects search: Hierarchical algorithm Future Work: More study on dynamic network Compare with other state-of-the-art approaches

20. Question How to deal with dynamic network is a challenge. There are network change situations like edge value change, what are other possible network changes? How would you like to deal with the dynamic network?