A speed-up of a known O(n 3 ) algorithm computing the period of a periodic orbit in max-min algebra is presented. If the critical components (or the transitive closure A + ) of the transition matrix A are known, the computational complexity of the algorithm is O(n 2 ). This is achieved by using only
Orbits in max–min algebra
✍ Scribed by Blanka Semančíková
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 283 KB
- Volume
- 414
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
Periodicity of matrix powers in max-min algebra is studied. The period of a matrix A is shown to be the least common multiple of the periods of at most n non-trivial strongly connected components in some threshold digraphs of A. An O(n3) algorithm for computing the period is described.
The problem of the strong regularity of a square matrix in a general max-min algebra is considered and a necessary and sufficient condition using the trapezoidal property is described. The results are valid without any restrictions on the underlying max-min algebra, concerning the density, or the bo