In the present paper we give a direct, shorter, proof of this theorem. Then we prove the existence of a half-integral optimal solution for the dual problem.
Oct 22, 2024 · We consider a network consisting of an undirected graph G=(V,E) with nonnegative integer capacities c(e) and costs a(e) on the edges e\in E, and ...
People also ask
What is the minimum cost network flow problem?
What is the minimum cost multi commodity flow problem?
Abstract. Let N = (G, T, c, a) be a network, where G is an undirected graph,. T is a distinguished subset of its vertices (called terminals), and each edge ...
cost a(e). The minimum cost maximum multi(commodity)flow problem ( * ) studied in this paper is to find a c-admissible multiflowfin G such that: (i) fis ...
Dec 31, 2009 · Generalizing known results on edge-capacitated multiflows, we show that the problem of finding a minimum cost multiflow among the feasible ...
Generalizing known results on edge-capacitated multiflows, we show that the problem of finding a minimum cost multiflow among the feasible multiflows of maximum ...
Apr 3, 2014 · In the general case, multi-commodity flow can have fractional optimum flow even if the capacities/costs are integers.
Dec 31, 2015 · I'm searching for an example digraph for the multi-commodity minimum cost flow problem with integer demand. There shouldn't be an integer but fractional ...
Sep 4, 2019 · In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network.
In this paper we discuss a number of recent and earlier results in the field of combinatorial optimization that concerns problems on minimum cost multiflows ( ...