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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
O W
AA
B
C
D
EF
H I J
KN
L
M
PQ
RS
TU
V
X
YZ
G1l G2
l
G3l
G4l
A
B
C
H J
KN
S
T
V
X
Z
G1l G2
l
G3l
G4l
32
3
1
1
1
2
45
4
4
3
11
2
2
2
1
1
2
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
AG
O W
AA
B
C
D
EF
H I J
KN
L
M
PQ
RS
TU
V
X
YZ
G1l G2
l
G3l
G4l
A
B
C
H J
KN
S
T
V
X
Z
G1l G2
l
G3l
G4l
32
3
1
1
1
2
45
4
4
3
11
2
2
2
1
1
2
Within-community routing (optimal route)
rebuild the search area:“nodes and edges of that subgraph”+” MCOMU(Gu
l)”
Routing Algorithm
AG
O W
AA
B
C
D
EF
H I J
KN
L
M
PQ
RS
TU
V
X
YZ
G1l G2
l
G3l
G4l
Between-community routing (heuristics)
Routing Algorithm
G1l G11
l
G2l
G5l
G3l
G4l
G6l
G8l
G9l
G10l
s t
p11
p12
c11
c12
G l7
long distance trips
… …G1l G11
l
G2l
G5l
G3l
G4l
G6l
G8l
G9l
G10l
s t
p11
p12
c11
c12
G l7
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.