On Integer Images of Max-plus Linear Mappings
Abstract
Let us extend the pair of operations (max,+) over real numbers to matrices in the same way as in conventional linear algebra. We study integer images of max-plus linear mappings. The question whether Ax (in the max-plus algebra) is an integer vector for at least one x has been studied for some time but polynomial solution methods seem to exist only in special cases. In the terminology of combinatorial matrix theory this question reads: is it possible to add constants to the columns of a given matrix so that all row maxima are integer? This problem has been motivated by attempts to solve a class of job-scheduling problems. We present two polynomially solvable special cases aiming to move closer to a polynomial solution method in the general case.
Cite
@article{arxiv.1709.09022,
title = {On Integer Images of Max-plus Linear Mappings},
author = {Peter Butkovic},
journal= {arXiv preprint arXiv:1709.09022},
year = {2017}
}