The multiroute maximum flow problem revisited

We are given a directed network G = (V, A, u) with vertex set V , arc set A, a source vertex s V , a destination vertex t V , a finite capacity vector u = {uij}ijA, and a positive integer m Z+. The multiroute maximum flow problem (m-MFP) generalizes the ordinary maximum flow problem by seeking a maximum flow from s to t subject to not only the regular flow conservation constraints at the vertices (except s and t) and the flow capacity constraints at the arcs, but also the extra constraints that any flow must be routed along m arc-disjoint s-t paths. In this paper, we devise two new combinatorial algorithms for m-MFP. One is based on Newton's method and another is based on augmenting-path technique. We also show how the Newton-based algorithm unifies two existing algorithms, and how the augmenting-path algorithm is strongly polynomial for case m = 2. Keywords Newton's method, augmenting-path, multiroute flow, parametric flow

• Type: Journal
• Year: 2006
• Where: NETWORKS
• Authors: Donglei Du, R. Chandrasekaran
• Keywords: Computer Networks, Maximum Flow, Maximum Flow Problem, Multiroute Maximum Flow, NETWORKS 2006