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

• Published in: Discrete Applied Mathematics Vol. 127; no. 3; pp. 651 - 656
• Main Authors: Gavalec, Martin, Plávka, Ján
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.05.2003; Amsterdam Elsevier; New York, NY
• Subjects: Applied sciences; Combinatorics; Combinatorics. Ordered structures; Eigenvalue; Exact sciences and technology; Graph theory; Mathematical programming; Mathematics; Monge matrix; Operational research and scientific management; Operational research. Management science; Sciences and techniques of general use; Eigenvalue; primary: 90C27; secondary: 05B35; Monge matrix; Matrix algebra; Permutation; Time; Graph theory; Computing; Properties; Algorithm; Computational complexity; Cycle; Standards; Result; Maximum; Algebra; Cyclic; Inverse; Cycle(graph)
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/S0166-218X(02)00395-5

An O( n 2) algorithm is described for computing the maximum cycle mean (eigenvalue) for n× n matrices, A=( a ij ) fulfilling Monge property, a ij + a kl ⩽ a il + a kj for any i< k, j< l. The algorithm computes the value λ( A)=max( a i 1 i 2 + a i 2 i 3 +⋯+ a i k i 1 )/ k over all cyclic permutations ( i 1, i 2,…, i k ) 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( n 3) time.