Parametric min-cuts analysis in a network

Abstract

AbstractThe all pairs minimum cuts problem in a capacitated undirected network is well known. Gomory and Hu showed that the all pairs minimum cuts are revealed by a min-cut tree that can be obtained by solving exactly (n−1) maximum flow problems, where n is the number of nodes in the network.In this paper we consider first the problem of finding parametric min-cuts for a specified pair of nodes when the capacity of an arc i is given by min{bi,λ}, where λ is the parameter, ranging from 0 to ∞. Next we seek the parametric min-cuts for all pairs of nodes, and achieve this by constructing min-cut trees for at most 2m different values of λ, where m is the number of edges in the network