Resolving Braess’s Paradox in Random Networks

Abstract

Braess's paradox states that removing a part of a network may improve the players' latency at equilibrium. In this work, we study the approximability of the best subnetwork problem for the class of random $\mathcal{G}_{n,p}$ instances proven prone to Braess's paradox by Roughgarden and Valiant, RSA 2010 and Chung and Young, WINE 2010. Our main contribution is a polynomial-time approximation-preserving reduction of the best subnetwork problem for such instances to the corresponding problem in a simplified network where all neighbors of s and t are directly connected by 0 latency edges. Building on this, we obtain an approximation scheme that for any constant e>0 and with high probability, computes a subnetwork and an e-Nash flow with maximum latency at most 1+eL i¾?+e, where L i¾? is the equilibrium latency of the best subnetwork. Our approximation scheme runs in polynomial time if the random network has average degree Opolyln n and the traffic rate is Opolyln ln n, and in quasipolynomial time for average degrees up to on and traffic rates of Opolyln n.