Submodular Unsplittable Flow on Trees

We study the Unsplittable Flow problem (UFP) on trees with a submodular objective function. The input to this problem is a tree with edge capacities and a collection of tasks, each characterized by a source node, a sink node, and a demand. A subset of the tasks is feasible if the tasks can simultaneously send their demands from the source to the sink without violating the edge capacities. The goal is to select a feasible subset of the tasks that maximizes a submodular objective function. Our main result is an O(k log n)-approximation algorithm for Submodular UFP on trees where k denotes the pathwidth of the given tree. Since every tree has pathwidth O(log n), we obtain an O(log2 n) approximation for arbitrary trees. This is the first non-trivial approximation guarantee for the problem, matching the best known approximation An extended abstract of this paper has been published in the Proceedings of the 18th International Conference on Integer Programming and Combinatorial Optimization (IPCO), LNCS, 2016. Partially supported by the Danish Council for Independent Research DFF-MOBILEX mobility grant. Work mostly done when the first, second and fourth authors were at Max Planck Institute for Informatics. B Parinya Chalermsook [email protected] Anna Adamaszek [email protected] Alina Ene [email protected] Andreas Wiese [email protected] 1 University of Copenhagen, Copenhagen, Denmark 2 Aalto University, Espoo, Finland 3 University of Warwick, Coventry, UK 4 Max-Planck-Institut für Informatik, Saarbrücken, Germany