Computing holes in semi-groups and its applications to transportation problems

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

An integer feasibility problem is a fundamental problem in many areas, such as operations research, number theory, and statistics. To study a family of systems with no nonnegative integer solution, we focus on a commutative semigroup generated by a finite set of vectors in $\Z^d$ and its saturation. In this paper we present an algorithm to compute an explicit description for the set of holes which is the difference of a semi-group $Q$ generated by the vectors and its saturation. We apply our procedure to compute an infinite family of holes for the semi-group of the $3\times 4\times 6$ transportation problem. Furthermore, we give an upper bound for the entries of the holes when the set of holes is finite. Finally, we present an algorithm to find all $Q$-minimal saturation points of $Q$.
Presentation has been improved according to comments by referees. This manuscript has been accepted to "Contributions to Discrete Mathematics"

Keywords

Combinatorics

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/226265

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607599
 http://arxiv.org/abs/math/0607599

Collections

arXiv