The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Selfish Routing and the Price of Anarchy
Selfish Routing and the Price of Anarchy
Algorithmic Game Theory
Speed-Up Techniques for the Selfish Step Algorithm in Network Congestion Games
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Engineering Route Planning Algorithms
Algorithmics of Large and Complex Networks
Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm
Journal of Experimental Algorithmics (JEA)
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
PHAST: Hardware-Accelerated Shortest Path Trees
IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium
Distributed time-dependent contraction hierarchies
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Processing crowd sourced sensor data: from data acquisition to application
Proceedings of the Sixth ACM SIGSPATIAL International Workshop on Computational Transportation Science
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The road traffic of an entire day for a certain region can be understood as a flow with sources and sinks on the road network. Traffic has the tendency to evade regularly clogged roads and other bottlenecks, especially with modern on-board navigation devices that are able to interpret traffic information. Assuming perfect knowledge for all drivers, one might suspect traffic to shape itself in a way such that all used routes between any two points on the road network have equal latency. Although these traffic patterns do not or very seldom occur in real life, they are a handy tool to predict the general traffic situation. For small networks, these patterns can be easily computed, but road networks that model entire countries are still a hurdle, because Dijkstra's algorithm does not scale. Thus the known techniques have only been applied to either small networks or small extracts of a much larger network. We solve this problem for country sized road networks by combining a gradient descent method to the problem with current research on fast route planning by exploiting the special properties of a routing algorithm called Contraction Hierarchies. The computation of the gradient needs a large number of shortest paths computations on the same weighted graph, which means that the expense for preprocessing can be amortized if the number of shortest paths computations is sufficiently large. This leads to dramatic overall speedup compared to running Dijkstra for each demand pair. Also, our study shows the robustness of Contraction Hierarchies on road networks at equilibrium state.