Let G = (V, E) be a graph with a source node s and a sink node t, |V | = n, |E| = m. For a given number k, the Maximum k–Splittable Flow Problem (MkSF) is to find an s, t–flow of maximum value with a flow decomposition using at most k paths. In the multicommodity case this problem generalizes disjoint paths problems and unsplittable flow problems. We provide a comprehensive overview of the complexity and approximability landscape of MkSF on directed and undirected graphs. We consider constant… CONTINUE READING