BibTeX
@MISC{Bolotashvili03solutionof,
author = {G. Bolotashvili},
title = {Solution of the Linear Ordering Problem (NP=P)},
year = {2003}
}
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Abstract
We consider the following problem n ∑ n∑ max i=1,i=j j=1 s. t. 0 � xij � 1, cijxij xij + xji = 1, 0 � xij + xjk − xik � 1, i = j, i = k, j = k, i, j, k = 1,..., n. We denote the corresponding polytope by Bn. The polytope Bn has integer vertices corresponding to feasible solutions of the linear ordering problem as well as non-integer vertices. We denote the polytope of integer vertices as Pn. Let us give an example of non-integer vertex in Bn and describe an exact facet cut. In what follows we will interested only in generating exact facet cuts. Fig. 1 shows a graph interpretation of a non-integer vertex [1], i1 i2 im j1 j2
