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

Authors:
Peter Butkovič;Karel Zimmermann
Affiliations:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK;Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

An algorithm for solving mxn systems of (max,+)-linear equations is presented. The systems have variables on both sides of the equations. After O(m^4n^4) iterations the algorithm either finds a solution of the system or finds out that no solution exists. Each iteration needs O(mn) operations so that the complexity of the presented algorithm is O(m^5n^5).