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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Veröffentlicht in:Discrete Applied Mathematics Jg. 103; H. 1; S. 167 - 175
Hauptverfasser: MOLNAROVA, M, PRIBIS, J
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Lausanne Elsevier B.V 15.07.2000
Amsterdam Elsevier
New York, NY
Schlagworte:
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
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Abstract 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.
AbstractList 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.
Author Pribiš, Ján
Molnárová, Monika
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  organization: Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University, Hlavnd 6, 04213 Košice, Slovakia
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Cites_doi 10.1016/0012-365X(73)90166-0
10.1007/978-3-642-48708-8
10.1016/0022-247X(77)90274-8
10.1016/S0166-218X(99)00174-2
10.1145/321105.321107
10.1016/S0166-218X(96)00079-0
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Issue 1
Keywords 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
Language English
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Snippet 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...
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SubjectTerms 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
Title Matrix period in max-algebra
URI https://dx.doi.org/10.1016/S0166-218X(99)00242-5
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