Efficient Route Computation on Road Networks Based on Hierarchical Communities

Efficient Route Computation on Road Networks Based on Hierarchical Communities

Qing Song, Xiaofan Wang

Department of Automation, Shanghai Jiao Tong University, Shanghai

Suzhou, October 17, 2010

Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

route planning systemin the internet(e.g. ditu.google.cn)

car navigation systems

logistics planning

traffic simulation

Shortest Path Problem

given a weighted, directed graph G=(V, E)with– n = |V| nodes,– m = |E| edgesgiven a source node s V and∈ target node t V∈task: determine the shortest path from s to t in G(if there is any path from s to t)

Shortest Path Problem— from graph theory

given a large, complicated road networkwhere– road intersections ---> nodes– roads ---> edges– user’s preferences

(e.g., time, distance, security, toll charges) ---> arc weights

task: select a reasonable route

Shortest Path Problem— from real life

the classic solution [1959]

Dijkstra Algorithm

Dijkstra s t

Bi-dijkstra s t

not practicablefor large graphs

improves the running time,but still too slow

O(nlogn+m) (Fibonacci heaps)

Road networks can be very largeWe want to compute the shortest path in a low timeWe can not preprocess and store all pairs shortest paths (APSP) due to memory limit, but some

Balance On-line/ Off-line

Off-line On-line

Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

Speed-up Techniques

s timportant

Hierarchical approach I:

road categories, road lengths, speed limits, ...

i.e., major roads and expressways (connected & sparse)

Hierarchical approach II:

effective partitioning—the number of boundary/ border nodes is uniform and minimized,

the subnetworks are

approximatively of equal size, …

(to reduce preprocessing cost)

Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

Tool: community detectionMerits:

1. extremely fast

2. can be applied to non-planar graph

3. retrieve more reasonable network structure—communities

4. dynamic scenario

Partitioning Tool & Merits

Hierarchical Graph Model

AG

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adjacent node/subgraph

border node

intercommunity edge

community edge (constructed)

“high-level community graph”

Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

Preprocessing:

1. community detection

2. construction of a two-level

graph hierarchy

3. local modifications

modified community edge

set MCOMU(Gul)

Routing Algorithm

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Within-community routing (optimal route)

rebuild the search area:“nodes and edges of that subgraph”+” MCOMU(Gu

l)”

Routing Algorithm

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Between-community routing (heuristics)

Routing Algorithm

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long distance trips

… …G1l G11

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Problem Description

Related Work

Hierarchical Graph Model

Routing Algorithm

Conclusion

Summary of Talk

light preprocessing, fast queries (merits)

worth extending to dynamic scenarios

study the algorithm performance under different community partitions and modularity values

try different community detection algorithms and choose the one with the best performance

Conclusion

Acknowledgement

This work was supported in part by the National Science Foundation of China under Grant 60731160629 and in part by the Major State Basic Research Development Program of China (973 Program) under Grant 2010CB731400.