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Fast Nearest Neighbor Search on Road Networks

Explore a novel approach for efficient kNN queries on road networks using SPIE trees and nd Indexing. The method simplifies network topology and boosts performance compared to traditional methods. Experimental results demonstrate significant improvements.

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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 • Sagar Uplanchiwar • MS Computer Science • Graduating Dec 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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