Parametric analysis of overall min-cuts and applications in undirected networks

Authors:
Y. P. Aneja;R. Chandrasekaran;K. P. K. Nair
Affiliations:
Odette School of Business, University of Windsor, Windsor, ON, Canada N9B 3P4;School of Computer Science, University of Texas at Dallas, Richardson, TX;Faculty of Administration, University of New Brunswick, Fredericton, NB, Canada E3B5A3
Venue:
Information Processing Letters
Year:
2003

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Abstract

The overall min-cut problem in a capacitated undirected network is well known. Recently Stoer and Wagner gave an elegant algorithm for finding such a cut. In this paper we present a parametric analysis of such a cut where the capacity of an arc {i, j} in the network is given by min{bi j, λ}, where λ is a parameter ranging from 0 to ∞. Letting function v(λ) denote the min-cut capacity, we develop an algorithm to describe v(λ) which involves at most n applications of Stoer and Wagner scheme, where n denotes the number of nodes in the network. We use v(λ) to determine an overall min-cut for multiroute flows as defined by Kishimoto. Such multi-route flows have interesting applications in communication networks.