Flows on Few Paths: Algorithms and Lower Bounds

Abstract. Classical network flow theory allows decomposition of flow into several chunks of arbitrary sizes traveling through the network on different paths. In the first part of this paper we consider the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only one path. We prove a lower bound of Ω(log m/ log log m) on the performance of a general class of algorithms for minimizing congestion where m is the number of edges in a graph. These algorithms start with a solution for the classical multicommodity flow problem, compute a path decomposition, and select one of its paths for each commodity in order to obtain an unsplittable flow. Our result matches the best known upper bound for randomized rounding – an algorithm of this type introduced by Raghavan and Thompson. The k-splittable flow problem is a generalization of the unsplittable flow problem where the number of paths is bounded for each commodity. We study a new varian...

• Type: Conference
• Year: 2004
• Where: ESA
• Authors: Maren Martens, Martin Skutella
• Keywords: ESA 2004, Multicommodity flow Problem, Unsplittable flow Problem, flow Problem