A penalized best‐response algorithm for nonlinear single‐path routing problems

This article is devoted to nonlinear single‐path routing problems, which are known to be NP‐hard even in the simplest cases. For solving these problems, we propose an algorithm inspired from Game Theory in which individual flows are allowed to independently select their path to minimize their own co...

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Vydané v:Networks Ročník 69; číslo 1; s. 52 - 66
Hlavní autori: Brun, Olivier, Prabhu, Balakrishna, Vallet, Josselin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Wiley Subscription Services, Inc 01.01.2017
Predmet:
Algorithms
Approximation
approximation algorithm
best response
Computer networks
Economic models
Game theory
Mathematical analysis
Nash equilibrium
Networks
nonlinear programming
Optimization
Routing
Routing (telecommunications)
single‐path routing
ISSN:0028-3045, 1097-0037
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Shrnutí:This article is devoted to nonlinear single‐path routing problems, which are known to be NP‐hard even in the simplest cases. For solving these problems, we propose an algorithm inspired from Game Theory in which individual flows are allowed to independently select their path to minimize their own cost function. We design the cost function of the flows so that the resulting Nash equilibrium of the game provides an efficient approximation of the optimal solution. We establish the convergence of the algorithm and show that every optimal solution is a Nash equilibrium of the game. We also prove that if the objective function is a polynomial of degree d ≥ 1 , then the approximation ratio of the algorithm is ( 2 1 / d − 1 ) − d . Experimental results show that the algorithm provides single‐path routings with modest relative errors with respect to optimal solutions, while being several orders of magnitude faster than existing techniques. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 52–66 2017
Bibliografia:This is an extended version of the paper A game‐theoretic algorithm for non‐linear single‐path routing problems” that appeared in the Proceedings of INOC 2015
The work of the third author was carried out while he was a doctoral student at LAAS.
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.21720