Note: Exponential behaviour of the Butkovič-Zimmermann algorithm for solving two-sided linear systems in max-algebra

Authors:
Marc Bezem;Robert Nieuwenhuis;Enric Rodríguez-Carbonell
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Technical University of Catalonia, Barcelona, Spain;Technical University of Catalonia, Barcelona, Spain
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

In [P. Butkovic, K. Zimmermann, A strongly polynomial algorithm for solving two-sided linear systems in max-algebra, Discrete Applied Mathematics 154 (3) (2006) 437-446] an ingenious algorithm for solving systems of two-sided linear equations in max-algebra was given and claimed to be strongly polynomial. However, in this note we give a sequence of examples showing exponential behaviour of the algorithm. We conclude that the problem of finding a strongly polynomial algorithm is still open.