LINEAR PROGRAMMING PROBLEMS WITH FUNDAMENTAL CUT MATRICES

Year 2018, Volume: 36 Issue: 3, 835 - 848, 01.09.2018

Firdovsi Sharıfov Hakan Kutucu

https://izlik.org/JA36MC89JP

Abstract

In the paper, we consider a linear programming problem with con-straint matrices whose rows are 0, 1 characteristics vectors of fundamental cuts in a given undirected graph G = (V, E). We prove that the simplex algorithm finds an optimal solution in at most m-n+1 (m = |E|, n = |V|) iterations. We also consider the question whether a given binary matrix is a 0, 1 characteristic vector of fundamental cuts in the graph G.

Keywords

Network design , submodular function , fundamental cut sets , linear programming

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