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 system in the internet (e.g. ditu.google.cn)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| edges given 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 network where – 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 practicable for large graphs improves the running time, but still too slow O(nlogn+m) (Fibonacci heaps)

Road networks can be very large We want to compute the shortest path in a low time We 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 t important

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 detection Merits: 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 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(G u l ) Routing Algorithm

Within-community routing (optimal route) rebuild the search area: “nodes and edges of that subgraph”+” MCOMU(G u l )” Routing Algorithm

Between-community routing (heuristics) Routing Algorithm long distance trips …

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 and in part by the Major State Basic Research Development Program of China (973 Program) under Grant 2010CB