The equation A ⊗ x = B ⊗ y over (max, +)

Authors:
R. A. Cuninghame-Green;P. Butkovic
Affiliations:
School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK;School of Mathematics and Statistics, The University of Birmingham, Edgbaston, B15 2TT Birmingham, UK
Venue:
Theoretical Computer Science
Year:
2003

Citing 0
Cited 9

A strongly polynomial algorithm for solving two-sided linear systems in max-algebra

Discrete Applied Mathematics
Eigenvectors of interval matrices over max-plus algebra

Discrete Applied Mathematics - Special issue: Max-algebra
Eigenvectors of interval matrices over max-plus algebra

Discrete Applied Mathematics
Communication: A strongly polynomial algorithm for solving two-sided linear systems in max-algebra

Discrete Applied Mathematics
Brief paper: On the control of max-plus linear system subject to state restriction

Automatica (Journal of IFAC)
Control of discrete event systems with respect to strict duration: Supervision of an industrial manufacturing plant

Computers and Industrial Engineering
Tropical linear-fractional programming and parametric mean payoff games

Journal of Symbolic Computation
The level set method for the two-sided max-plus eigenproblem

Discrete Event Dynamic Systems
On the integer max-linear programming problem

Discrete Applied Mathematics

Quantified Score

Hi-index	5.23

Visualization

Abstract

For the two-sided homogeneous linear equation system A ⊗ x = B ⊗ y over (max, +), with no infinite rows or columns in A or B, an algorithm is presented which converges to a finite solution from any finite starting point whenever a finite solution exists. If the finite elements of A, B are all integers, convergence is in a finite number of steps, for which a precise bound can be calculated if moreover one of A, B has only finite elements. The algorithm is thus pseudopolynomial in complexity.