An O(n2) algorithm for maximum cycle mean of Monge matrices in max-algebra

Authors:
Martin Gavalec;Ján Plávka
Affiliations:
Department of Information Technologies, Faculty of Informatics and Management, University Hradec Králové, V. Nejedlého 573, 50003 Hradec Králové, Czech Republic;Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University in Kosice, B. Nemcovej 32, 04200 Kosice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

An O(n2) algorithm is described for computing the maximum cycle mean (eigenvalue) for n × n matrices, A = (aij) fulfilling Monge property, aij + akl ≤ ail + akj for any i . The algorithm computes the value λ(A) = max(ai1i2) + +ai2j3 + ... + aikj1/k over all cyclic permutations (i1, i2,..., ik) of subsets of the set {1,2,...,n). A similar result is presented for matrices with inverse Monge property. The standard algorithm for the general case works in O(n3) time.