On Integer Images of Max-plus Linear Mappings

Peter Butkovic

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arXiv · 1709.09022

On Integer Images of Max-plus Linear Mappings

Peter Butkovic

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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.

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BibTeX RIS

Peter Butkovic. 2017-09-26. On Integer Images of Max-plus Linear Mappings. https://arxiv.org/abs/1709.09022

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