Some insight into characterizations of minimally nonideal matrices |
| |
Authors: | Gabriela R Argiroffo Silvia M Bianchi Graciela L Nasini |
| |
Institution: | (1) Facultad de Ciencias Exactas, Ingenieria y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina |
| |
Abstract: | Lehman (Polyhedral combinatorics 1 of DIMACS series in discrete math. and theoretical computer science, pp 101–105, 1990) described some conditions regular
minimally nonideal (mni) matrices must satisfy. Although, there are few results on sufficient conditions for mni matrices.
In most of these results, the covering polyhedron must have a unique fractional extreme point. This condition corresponds
to ask the matrix to be the blocker of a near-ideal matrix, defined by the authors in a previous work (2006). In this paper
we prove that, having the blocker of a near-ideal matrix, only a few very easy conditions have to be checked in order to decide
if the matrix is regular mni. In doing so, we define the class of quasi mni matrices, containing regular mni matrices, and
we find a generalization on the number of integer extreme points adjacent to the fractional extreme point in the covering
polyhedron. We also give a relationship between the covering and stability number of regular mni matrices which allows to
prove when a regular mni matrix can be a proper minor of a quasi mni.
Partially supported by CONICET Grant PIP 2807/2000 (Argentina) and by CNPq/PROSUL Grant 490333/2004-4 (Brasil). |
| |
Keywords: | Minimally nonideal matrix Set covering polyhedra |
本文献已被 SpringerLink 等数据库收录! |
|