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New Facets of the Linear Ordering Polytope (1995)
| Citations: | 13 - 1 self |
BibTeX
@MISC{Bolotashvili95newfacets,
author = {G. Bolotashvili and M. Kovalev and E. Girlich},
title = {New Facets of the Linear Ordering Polytope},
year = {1995}
}
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Abstract
The linear ordering problem has many applications and was studied by many authors (see [5, 9, 12] for survey). One approach to solve this problem, the so-called cutting plane method [8, 14] derives facet-defining inequalities, which are violated by current nonfeasible solution and adds them to the system of inequalities of current linear programming problem. We present a method (rotation method) for generating new facets of polyhedra by using already known ones. The rotation method for the linear ordering polytope generalizes facets induced by subgraphs called m-fences, Mobius ladders and Zm -facets introduced by Reinelt [12], (m; k)- fences introduced by Bolotashvily [1] and t-reinforced m-fences introduced by Leung and Lee [10]. We introduce ten collections of inequalities representing facets of the linear ordering polytope. Among them there are three that coincide with earlier known ones: m-wheel-facets introduced by Reinelt [12], augmented m-fences introduced by McLennan [11] and...
Keyphrases
new facet linear ordering polytope rotation method so-called cutting plane method many application ten collection current linear programming problem linear ordering problem derives facet-defining inequality zm facet current nonfeasible solution many author t-reinforced m-fences mobius ladder
