Approximating Congestion + Dilation in Networks via "Quality of Routing” Games

A classic optimization problem in network routing is to minimize C + D, where C is the maximum edge congestion and D is the maximum path length (also known as dilation). The problem of computing the optimal C* + D* is NP-complete even when either C* or D* is a small constant. We study routing games in general networks where each player i selfishly selects a path that minimizes Ci + Di the sum of congestion and dilation of the player's path. We first show that there are instances of this game without Nash equilibria. We then turn to the related quality of routing (QoR) games which always have Nash equilibria. QoR games represent networks with a small number of service classes where paths in different classes do not interfere with each other (with frequency or time division multiplexing). QoR games have O(log4 n) price of anarchy when either C* or D* is a constant. Thus, Nash equilibria of QoR games give poly-log approximations to hard optimization problems.

[1]  Friedhelm Meyer auf der Heide,et al.  Universal algorithms for store-and-forward and wormhole routing , 1996, STOC '96.

[2]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[3]  Marios Mavronicolas,et al.  A new model for selfish routing , 2008, Theor. Comput. Sci..

[4]  Elias Koutsoupias,et al.  The price of anarchy of finite congestion games , 2005, STOC '05.

[5]  Rolf H. Möhring,et al.  Strong Nash Equilibria in Games with the Lexicographical Improvement Property , 2009, WINE.

[6]  Berthold Vöcking,et al.  Tight bounds for worst-case equilibria , 2002, SODA '02.

[7]  Marios Mavronicolas,et al.  Nash Equilibria in Discrete Routing Games with Convex Latency Functions , 2004, ICALP.

[8]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet , 2001, ICALP.

[9]  Berthold Vöcking,et al.  Selfish Traffic Allocation for Server Farms , 2010, SIAM J. Comput..

[10]  Costas Busch,et al.  Atomic routing games on maximum congestion , 2006, Theor. Comput. Sci..

[11]  Paul G. Spirakis,et al.  The structure and complexity of Nash equilibria for a selfish routing game , 2002, Theor. Comput. Sci..

[12]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[13]  L. Shapley,et al.  Potential Games , 1994 .

[14]  Ariel Orda,et al.  Atomic Resource Sharing in Noncooperative Networks , 2001, Telecommun. Syst..

[15]  Marios Mavronicolas,et al.  The price of anarchy for polynomial social cost , 2004, Theor. Comput. Sci..

[16]  Yuval Rabani,et al.  Distributed packet switching in arbitrary networks , 1996, STOC '96.

[17]  Tim Roughgarden,et al.  How bad is selfish routing? , 2002, JACM.

[18]  Bruce M. Maggs,et al.  Packet routing and job-shop scheduling inO(congestion+dilation) steps , 1994, Comb..

[19]  Tim Roughgarden,et al.  Bounding the inefficiency of equilibria in nonatomic congestion games , 2004, Games Econ. Behav..

[20]  Rafail Ostrovsky,et al.  Universal O(congestion + dilation + log1+εN) local control packet switching algorithms , 1997, STOC '97.

[21]  Tim Roughgarden,et al.  Selfish routing with atomic players , 2005, SODA '05.

[22]  Christian Scheideler,et al.  Locally efficient on-line strategies for routing packets along fixed paths , 1999, SODA '99.

[23]  Marios Mavronicolas,et al.  Computing Nash Equilibria for Scheduling on Restricted Parallel Links , 2004, STOC '04.

[24]  Aravind Srinivasan,et al.  A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria , 1997, STOC '97.

[25]  Ariel Orda,et al.  Bottleneck Routing Games in Communication Networks , 2007, IEEE J. Sel. Areas Commun..

[26]  José R. Correa,et al.  Sloan School of Management Working Paper 4447-03 November 2003 Computational Complexity , Fairness , and the Price of Anarchy of the Maximum Latency Problem , 2003 .

[27]  Paul G. Spirakis,et al.  Selfish Unsplittable Flows , 2004, ICALP.

[28]  Tim Roughgarden.  The maximum latency of selfish routing , 2004, SODA '04.

[29]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[30]  Paul G. Spirakis,et al.  The Price of Selfish Routing , 2001, STOC '01.

[31]  Paul G. Spirakis,et al.  Approximate Equilibria and Ball Fusion , 2003, Theory of Computing Systems.

[32]  Bruce M. Maggs,et al.  Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules , 1999, Comb..

[33]  Éva Tardos,et al.  Near-optimal network design with selfish agents , 2003, STOC '03.