On the Hardness of Network Design for Bottleneck Routing Games

  • Dimitris Fotakis
  • Alexis C. Kaporis
  • Thanasis Lianeas
  • Paul G. Spirakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)

Abstract

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 ε > 0. 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dimitris Fotakis
    • 1
  • Alexis C. Kaporis
    • 2
  • Thanasis Lianeas
    • 1
  • Paul G. Spirakis
    • 3
    • 4
  1. 1.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Department of Information and Communication Systems EngineeringUniversity of the AegeanSamosGreece
  3. 3.Department of Computer Engineering and InformaticsUniversity of PatrasPatrasGreece
  4. 4.Computer Technology Institute and Press - Diophantus N. Kazantzaki Str.PatrasGreece

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