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Scalable Network Distance Browsing in Spatial DatabaseSamet, H., Sankaranarayanan, J., and Alborzi H.
Proceedings of the 2008 ACM SIGMOD international Conference on Management of Data
Presented by:Don Eagan
Chintan Patelhttp://www-users.cs.umn.edu/~cpatel/8715.html
Outline• Motivation• Problem Statement• Proposed Approach• Other Approaches• Evaluation• Our Comments• Questions
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
Challenges• Real-time response• Calculating all pairs shortest path is costly • Storing pre-computed naïvely doesn’t solve the problem • Scalability
Contribution• Efficient path encoding• Efficient retrieval• Abstracting shortest path calculation from domain queries
Key Concepts• Spatial Networks• Nearest Network Neighbor• Quad Tree• Morton Blocks• Decoupling• Scalability• Pre-computing
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
Proposed Approach• Pre-compute shortest paths• Store and Retrieve Efficiently
N = Number of vertices, M = Number of edges, s = Length of the shortest path
Method Space Retrieval Time
Explicit O(N^3) O(1)
Dijkstra O(N + M) O(M + N log N)
SLIC O(N √N) O(s log N)
Path Encoding• Path coherence• Vertices in close proximity share portion of the shortest paths to
them from distant sources
Path Encoding• Path coherence• Vertices in close proximity share portion of the shortest paths to
them from distant sources
Path Encoding• Path coherence• Vertices in close proximity share portion of the shortest paths to
them from distant sources
Path Encoding• Path coherence• Vertices in close proximity share portion of the shortest paths to
them from distant sources
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•
Our Comments• We Liked:• Decoupling shortest path and neighbor calculation• Space reduction approach
• Scalable
• Correctness proofs• Detailed discussion about KNN variants
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