# Powers of matrices over an extremal algebra with applications to periodic graphs

Article

- Received:
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DOI: 10.1007/BF01199464

- Cite this article as:
- Nachtigall, K. Mathematical Methods of Operations Research (1997) 46: 87. doi:10.1007/BF01199464

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## Abstract

Consider the extremal algebra=(ℝ∪{∞},min,+), using + and min instead of addition and multiplication. This extremal algebra has been successfully applied to a lot of scheduling problems. In this paper the behavior of the powers of a matrix over is studied. The main result is a representation of the complete sequence (

*A*^{m})_{m∈ℕ}which can be computed within polynomial time complexity. In the second part we apply this result to compute a minimum cost path in a 1-dimensional periodic graph.### Key words

Extremal AlgebraPeriodic GraphsMinimum Cost Paths## Copyright information

© Physica-Verlag 1997