Computing holes in semi-groups and its applications to transportation problems
摘要
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 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 generated by the vectors and its saturation. We apply our procedure to compute an infinite family of holes for the semi-group of the 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 -minimal saturation points of .
引用
@article{arxiv.math/0607599,
title = {Computing holes in semi-groups and its applications to transportation problems},
author = {Raymond Hemmecke and Akimichi Takemura and Ruriko Yoshida},
journal= {arXiv preprint arXiv:math/0607599},
year = {2009}
}
备注
Presentation has been improved according to comments by referees. This manuscript has been accepted to "Contributions to Discrete Mathematics"