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Abstract

Abstract: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 t 1 , . . . ,t k ∈ V corresponding to k commodities; we denote it I = (s;t 1 , . . . ,t k ). In the single source multicommodity multiroute flow problem, we are given an instance I = (s;t 1 , . . . ,t k ) and an integer h ≥ 1, and the objective is to maximize the * A preliminary version of this work appeared in