A stronger bound on Braess's Paradox
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Bottleneck links, variable demand, and the tragedy of the commons
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Atomic routing games on maximum congestion
Theoretical Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The hardness of selective network design for bottleneck routing games
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Wardrop equilibria and price of stability for bottleneck games with splittable traffic
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Braess's paradox, fibonacci numbers, and exponential inapproximability
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The hardness of network design for unsplittable flow with selfish users
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Bottleneck Routing Games in Communication Networks
IEEE Journal on Selected Areas in Communications
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In routing games, the network performance at equilibrium can be significantly improved if we remove some edges from the network. This counterintuitive fact, a.k.a. Braess's paradox, gives rise to the network design problem, where we seek to recognize routing games suffering from the paradox, and to improve the equilibrium performance by edge removal. In this work, we investigate the computational complexity and the approximability of network design for non-atomic bottleneck routing games, where the individual cost of each player is the bottleneck cost of her path, and the social cost is the bottleneck cost of the network. We first show that bottleneck routing games do not suffer from Braess's paradox either if the network is series-parallel, or if we consider only subpath-optimal Nash flows. On the negative side, we prove that even for games with strictly increasing linear latencies, it is NP-hard not only to recognize instances suffering from the paradox, but also to distinguish between instances for which the Price of Anarchy (PoA) can decrease to 1 and instances for which the PoA is Ω(n0.121) and cannot improve by edge removal. Thus, the network design problem for such games is NP-hard to approximate within a factor of O(n0.121−ε), for any constant ε0. On the positive side, we show how to compute an almost optimal subnetwork w.r.t. the bottleneck cost of its worst Nash flow, when the worst Nash flow in the best subnetwork routes a non-negligible amount of flow on all edges. The running time is determined by the total number of paths, and is quasipolynomial if the number of paths is quasipolynomial.