The algorithms proposed in the present paper efficiently solve the problem of finding a lexicographically optimal flow in a network with multiple sources and sinks, which is a special case of the problem considered here.Expand

This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question posed in 1981 by Grötschel, Lovász, and Schrijver. The algorithm employs… Expand

It is proved that a reservation value (or utility) function satisfies the gross substitutes condition if and only if it is anM?-concave function defined on the unit-hypercube, which is a discrete concave function recently introduced by Murota and Shioura (1999).Expand

The present paper points out that the entropy function h is a β -function, i.e., a monotone non-decreasing and submodular function with h(O) = 0 and that the pair ( E, h ) is a polymatroid.Expand

We consider an application of the minimum-norm-point algorithm to submodular function minimization. Although combinatorial polynomial algorithms for submodular function minimization (SFM) have… Expand

The present paper shows that for any submodular functionf on a crossing family with, if the polyhedron is nonempty, then there exist a unique distributive lattice with and a unique submodular… Expand

A convex (or concave) conjugate function of a submodular (or supermodular) function is defined and a Fenchel-type min-max theorem for sub modular and super modular functions is shown.Expand

Given a capacitated network with the entrance· vertex set VI and the exit-vertex set V2 on which polymatroids are defmed, an independent flow is a flow in the network such that a vector corresponding… Expand

This paper presents an O(nlog2n) time algorithm for the sink location problem, in a dynamic network of tree structure where n is the number of vertices in the network, and shows that the quickest transshipment problem can be solved in O( nlog2 n) time if a given network is a tree and has a single sink.Expand