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. Problem Road Networks

5. Problem Road Networks – Nearest Neighbor Search

6. Existing Solutions
Voronoi
Dijkstra’s

7. Motivation Dijkstra’s 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 Reduction The Elements of reduction
Shortest Path Trees (SPT)
Distance between root and other nodes is minimized

10. Network Reduction The 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 Node Deletion
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. Performance Network Reduction
With ~430K nodes, only 1571 SPIEs made

22. Performance nd 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. Performance NN Search Result
From average of 2000 trials

24. Performance KNN Search Result
For p=0.01 dataset on real road network

25. Performance Summary 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