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Fast Nearest Neighbor Search on Road Networks

Introducing a novel technique for kNN search on network structures, reducing complexity, enhancing performance, and analyzing cost models.

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Fast Nearest Neighbor Search on Road Networks

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  1. Fast Nearest Neighbor Search on Road Networks Haibo Hu, Dik Lun Lee, and Jianliang Xu Hong Kong Univ. of Science & Technology Hong Kong Baptist University

  2. About Myself • Martin Ahrens • 4th Year • Interested in AI, Game Development, Databases, Info Sec • Graduating May 2008

  3. Presentation Outline • Problem • Existing Solutions • Motivation for new work • Network Reduction, SPH, SPIE • nd (nearest descendants) Index • Updates • Cost Models • Performance • Conclusions

  4. ProblemRoad Networks

  5. ProblemRoad Networks – Nearest Neighbor Search

  6. Existing Solutions • Voronoi • Dijkstra’s

  7. Motivation • Voronoi • Unwieldy for denser/vast data • Dijkstra’s • Too many node visits on large/sparser data

  8. Network Reduction • Objectives • Reduce the number of edges while preserving network distances • Replace complex graph topology with simpler structures (trees).

  9. Network ReductionThe Elements of reduction • Shortest Path Trees (SPT) • Distance between root and other nodes is minimized

  10. Network ReductionThe Elements of reduction • Are Shortest Path Tree (SPT) networks inefficient for road networks? • Degree of vertices in a road network are typically >= 3. • The length of the shortest circuits are still usually long • These reasons justify the reduction of road networks to SPT pieces

  11. SPH • SPH means Shortest Path Trees with Horizontal Edges Specified to reduce number of connected trees • Like SPT but with another condition • Allow sibling-sibling connections (horizontal edges) within trees

  12. SPH Algorithm

  13. NN search on a tree

  14. SPIE • An SPIE is an SPH with another condition • SPIE SPH with ‘Triangular Inequality’ Edges Shortest Path between two nodes in a tree is guaranteed to contain exactly one horizontal edge between ancestors of the two nodes

  15. NN search on SPIE

  16. nd Index – nearest descendant • Very simple operation • For every node in the tree, extract the nearest descendant data node (point of interest) down the tree representation of the road.

  17. SPIE Algorithms

  18. Updates • Node Insertion • Insert into SPIE containing adjacent node • Node Deletion • Rebuild local SPIE • Edge Insertion/Deletion non-trivial depending on specifics of the edge, but is still relatively inexpensive • Edge re-weighting is like above • Data Point Insertion/Deletion only requires change of nd Index of local SPIE tree

  19. Cost Models • I will just provide an overview of insights • Even in a 2D uniform grid (city blocks) there is still a 25% benefit by the reduction model • Nearest Neighbor search by traditional means is exponential while SPIE NN search is linear to the average distance from a node to a NN • Number of node accesses in nd index is much less than in the traditional approach

  20. Performance • Experimented with the algorithms on two sets of data • Artificial network with ~180K nodes, exponential distribution of node degrees, edge weights random 1 through 10 • Digital Chart of the World (DCW) containing ~600K railroads and roads in the Americas. ~400K nodes • Test system: C++ on Win32 platform, 2.4 Ghz P4, 512 MB RAM, 4Kb page size

  21. PerformanceNetwork Reduction • With ~430K nodes, only 1571 SPIEs made

  22. Performancend Index Construction • p represents density of random datasets • Ignores one-time construction of SPIE graph • ~8 MB, created in ~300 seconds • Almost constant construction time of nd Index

  23. PerformanceNN Search Result • From average of 2000 trials

  24. PerformanceKNN Search Result • For p=0.01 dataset on real road network

  25. PerformanceSummary • Network Reduction and nd Indexing • Simplify network topology in a decent one-time cost • Create light-weight (CPU and mem) nd Index • Perform well on (k)NN queries of varying data • Perform well on kNN for various k values

  26. Conclusions • Overview • New network kNN search technique created • Reduction of network to a set of interconnected tree structures (SPIE) • nd index created per SPIE to make kNN search on SPIE follow predetermined path, and faster • Cost Models and Experimental Results both show improvement upon network-expansion (Dijkstra’s) and solution-based (Voronoi) system for most network topologies and distributions • Future plans are to redesign structure in place of SPIE trees

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