On the approximation of the single source k-splittable flow problem

This work deals with the minimum congestion single-source k-splittable flow problem: given a network and a set of terminal pairs sharing a common source node, the aim is to route concurrently all demands using at most k   supporting paths for each commodity and minimizing the congestion on arcs. Dinitz et al. proposed in [Y. Dinitz, N. Garg, M.X. Goemans, On the single-source unsplittable flow problem, Combinatorica 19 (1999) 17–41] the best known constant factor approximated algorithm for the case of k=1k=1, namely the single source unsplittable case. Here we consider an adaptation of such an algorithm to the k-splittable case. Moreover, we propose a heuristic improvement of the first step of this algorithm, that provides experimentally better results without affecting the approximation guarantee of the algorithm.