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 Hρ-approximation algorithm, where ρ is the sum of the ranks of the polymatroids and Hρ denotes the ρ-th harmonic number. The approximation guarantee is best possible up to a constant factor and solves an open problem of Ackermann et al. (2008).