Single Source Multiroute Flows and Cuts on Uniform Capacity Networks

For an integer h 1, an elementary h-route flow is a flow along h edge disjoint paths between a source and a sink, each path carrying a unit of flow, and a single commodity h-route flow is a non-negative linear combination of elementary h-route flows. An instance of a single source multicommodity flow problem for a graph G = (V, E) consists of a source vertex s V and k sinks t1, . . . , tk V corresponding to k commodities; we denote it I = (s; t1, . . . , tk). In the single source multicommodity multiroute flow problem, we are given an instance I = (s; t1, . . . , tk) and an integer h 1, and the objective is to maximize the total amount of flow that is transferred from the source to the sinks so that the capacity constraints are obeyed and, moreover, the flow of each commodity is an h-route flow. We study the relation between classical and multiroute single source flows on undirected networks with uniform capacities and we provide a tight bound. In particular, we prove the followin...

• Type: Journal
• Year: 2008
• Where: TOC
• Authors: Henning Bruhn, Jakub Cerný, Alexander Hall, Petr Kolman, Jiri Sgall
• Keywords: Elementary H-route Flows, H-route Flow, Single Source Multicommodity, TOC 2008