Matrix period in max-algebra

Periodicity of matrices in max-algebra is studied. A necessary and sufficient condition is found for a given matrix to be almost periodic. The period of a matrix is shown to be the least common multiple of the high periods of all non-trivial highly connected components in the corresponding digraph o...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 103; no. 1; pp. 167 - 175
Main Authors: MOLNAROVA, M, PRIBIS, J
Format: Journal Article
Language:English
Published: Lausanne Elsevier B.V 15.07.2000
Amsterdam Elsevier
New York, NY
Subjects:
Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Linear and multilinear algebra, matrix theory
Mathematical logic, foundations, set theory
Mathematics
Matrix period
Max-algebra
Sciences and techniques of general use
Set theory
secondary 05C50
primary 04A72
15A33
Max-algebra
Matrix period
Necessary and sufficient condition
Max algebra
Connected component
NP complete problem
Connectedness
Dynamical system
Directed graph
Complexity
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:Periodicity of matrices in max-algebra is studied. A necessary and sufficient condition is found for a given matrix to be almost periodic. The period of a matrix is shown to be the least common multiple of the high periods of all non-trivial highly connected components in the corresponding digraph of A. An O(n 3) algorithm for computing the exact value of the matrix period for a given matrix is described.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(99)00242-5