A Logarithmic Approximation for Polymatroid Congestion Games

We study the problem of computing a social optimum in polymatroid congestion games, where the strategy space of every player consists of a player-specific integral polymatroid base polyhedron on a set of resources. For non-decreasing cost functions we devise an H-rho-approximation algorithm, where rho is the sum of the ranks of the polymatroids and H-rho denotes the rho-th harmonic number. The approximation guarantee is best possible up to a constant factor and solves an open problem of Ackermann et al. (2008). (C) 2016 Elsevier B.V. All rights reserved.