Powers of matrices over an extremal algebra with applications to periodic graphs Authors Karl Nachtigall Institut für Flugführung DLR Article

Received: 15 September 1995 Revised: 15 May 1996 DOI :
10.1007/BF01199464

Cite this article as: Nachtigall, K. Mathematical Methods of Operations Research (1997) 46: 87. doi:10.1007/BF01199464
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 Algebra Periodic Graphs Minimum Cost Paths

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