Multi-terminal multipath flows: synthesis*1

Abstract

Given an undirected network G ≡[ N , E ], a source–sink pair of nodes ( s , t ) in N , a non-negative number u i , j representing the capacity of edge ( i , j ) for each ( i , j )∈ E , and a positive integer q , an “elementary q -path flow” from s to t is defined as a flow of q units from s to t , with one unit of flow along each path in a set of q edge-disjoint s – t paths. A q -path flow from s to t is a non-negative linear combination of elementary q -path flows from s to t . In this paper we provide a strongly polynomial combinatorial algorithm for designing an undirected network with minimum total edge capacity which is capable of meeting, non-simultaneously, a given set of symmetric q -path flow requirements between all pairs of nodes. This extends the previous work on network synthesis.