Equilibrium Computation in Atomic Splittable Singleton Congestion Games

We devise the first polynomial time algorithm computing a pure Nash equilibriumfor atomic splittable congestion games with singleton strategies and player-specificaffine cost functions. Our algorithm is purely combinatorial and computes the exactequilibrium assuming rational input. The idea is to compute a pure Nash equilibriumfor an associated integrally-splittable singleton congestion game in which the players canonly split their demands in integral multiples of a common packet size. While integralgames have been considered in the literature before, no polynomial time algorithmcomputing an equilibrium was known. Also for this class, we devise the first polynomialtime algorithm and use it as a building block for our main algorithm.