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

Karl Nachtigall

Mathematical Methods of Operations Research, 1997, vol. 46, issue 1, 87-102

Abstract: Consider the extremal algebra[Figure not available: see fulltext.]=(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[Figure not available: see fulltext.] 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. Copyright Physica-Verlag 1997

Keywords: Extremal Algebra; Periodic Graphs; Minimum Cost Paths (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/BF01199464

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