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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. Outline.
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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 Patel http://www-users.cs.umn.edu/~cpatel/8715.html
Outline • Motivation • Problem Statement • Proposed Approach • Other Approaches • Evaluation • Our Comments • Questions
Motivation • Growing Popularity of Online Mapping Services
Motivation • Real Time Shortest Paths
Motivation • Static Network, Variable Queries • Find Gas Stations, Hotels, Markets etc.
Motivation • Static Network, Variable Queries • Find Gas Stations, Hotels, Markets etc.
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
Shortest Path • Dijkstra’s algorithm • Doesn’t work for real-time queries • Computationally expensive
Proposed Approach • Pre-compute shortest paths • Store and Retrieve Efficiently N = Number of vertices, M = Number of edges, s = Length of the shortest path
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
Path Encoding • Quadtree: Decompose until all vertices in block have same color
How is space reduced? • Capturing boundaries !
Path Retrieval • Retrieve quadtree corresponding to s
Path Retrieval • Find connected node t in the quadtree containing d
Path Retrieval • Repeat the process
K-nearest Neighbor • Set of objects • Pre-computed paths (quadtree)
K-nearest Neighbor • K = 2
K-nearest Neighbor • Queue1: m a b • Queue2: a b
K-nearest Neighbor • Queue1: a g e b f • Queue2: a g
K-nearest Neighbor • Queue1: a g e • Queue2: a g
K-nearest Neighbor • Return a and g
Other Approaches • IER: Incremental Euclidian Restriction • Based on Euclidian distance • Dijkstra’s algorithm to get network distance • INE: Incremental. Network Expansion • Dijkstra'salgorithm with a buffer L containing the k nearest neighbors seen so far in terms of network distance
Evaluation • Micro benchmark • Synthetic Data
Evaluation • Real Data Set: Major Road of the USA
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
Discussion • Other use cases? • Real Application: How to overcome assumptions?
Questions ? ? ?