On the linear relaxation of the s-t-cut Problem with Budget Constraints

Abstract

We consider in this paper a generalization of the minimum s-t cut problem. Suppose we are given a directed graph G(V,A) with two distinguished nodes s and t, k non-negative arcs cost functions (formula presented), and (formula presented)budget bounds (formula presented) where k is a constant. The goal is to find a (formula presented) cut C satisfying budget constraints (formula presented), and whose cost (formula presented) is minimum. We study the linear relaxation of the problem and give necessary and sufficient conditions for which it has an integral optimal basic solution.