Given a finite set E of r andom variables, the entropy function h on E is a mapp ing f rom the set of all subsets of E into the set of all nonnegative real number s such that for each A C_ E h(A) isâ€¦ (More)

We consider an application of the minimum-norm-point algorithm to submodular function minimization. Although combinatorial polynomial algorithms for submodular function minimization (SFM) haveâ€¦ (More)

This paper deals with the problem of finding a minimum-cost vertex subset S in an undirected network such that for each vertex v we can send d(v) units of flow from S to v. Although this problem isâ€¦ (More)

In the present paper we consider applications of the minimum-norm-point algorithm to submodular function minimization and linear programming. Although combinatorial polynomial algorithms forâ€¦ (More)

Given a capacitated network with the entranceÂ· 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 correspondingâ€¦ (More)

In this paper, we consider source location problems and their generalizations with three connectivity requirements (arc-connectivity requirements Î» and two kinds of vertex-connectivity requirements Îºâ€¦ (More)