Mathematical Methods of Operations Research

, Volume 46, Issue 1, pp 87–102

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

Authors

  • Karl Nachtigall
    • Institut für FlugführungDLR
Article

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 (Am)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