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The minimum weight t-composition of an integer

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Abstract

Let p and t, p ≥ t, be positive integers. A t-composition of p is an ordered t-tuple of positive integers summing p. If T = (s 1 , s 2 , . . . , s t ) is a t-composition p and W is a p − (t − 1) × t matrix, then \( W(T) = \sum\limits_{k = 1}^t {{w_{{s_k}k}}} \) is called the weight of the t-composition T. We show that finding a minimum weight t-composition of p can be reduced to the determination of the shortest path in a certain digraph with O(tp) vertices. This study was motivated by a problem arising from the automobile industry, and the presented result is useful when dealing with huge location problems.

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Authors and Affiliations

  1. Departamento de Matemática da Universidade de Aveiro, Aveiro, Portugal

    D. M. Cardoso

  2. Centro de Estudos Florestais, Instituto Superior de Agronomia, Technical University of Lisbon, Lisboa, Portugal

    J. O. Cerdeira

Authors
  1. D. M. Cardoso
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  2. J. O. Cerdeira
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Correspondence to D. M. Cardoso.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.

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Cardoso, D.M., Cerdeira, J.O. The minimum weight t-composition of an integer. J Math Sci 182, 210–215 (2012). https://doi.org/10.1007/s10958-012-0741-3

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