Advertisement

Journal of Mathematical Sciences

, Volume 182, Issue 2, pp 210–215 | Cite as

The minimum weight t-composition of an integer

  • D. M. CardosoEmail author
  • J. O. Cerdeira
Article

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.

Keywords

Short Path Location Problem Active Option Minimum Weight Inclusion Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Agra, D. M. Cardoso, J. O. Cerdeira, M. Miranda, and E. Rocha, The minimum weight spanning star forest model of the optimal diversity management problem, Cadernos de Matemática, Universidade de Aveiro CM07 (I-08) (2007).Google Scholar
  2. 2.
    P. Avella, M. Boccia, C. D. Martino, G. Oliviero, and A. Sforza, “A decomposition approach for a very large scale optimal diversity management problem,” 3, No. 1, 23–37 (2005).Google Scholar
  3. 3.
    O. Briant, Étude théorique et numérique du problème de la gestion de la diversité, Ph.D. thesis, Institut National Polytechnique de Grenoble (2000).Google Scholar
  4. 4.
    O. Briant and D. Naddef, “The optimal diversity management problem,” Oper. Res., 52, No. 4, 515–526, (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik 1, 269–271 (1959).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    D. Hochbaum and D. Shmoys, “A best possible heuristic for the k-center problem,” Math. Oper. Res., 10, 180–184 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    P. Jarvinen, J. Rajala, and H. Sinervo, “A branch and bound algorithm for seeking the p-median,” Oper. Res., 20, 173–178 (1972).CrossRefGoogle Scholar
  8. 8.
    O. Kariv and S. L. Hakini, “An algorithmic approach to network location problems. Part 1: The p-Centers,” SIAM J. Appl. Math., 37, 513–538 (1979).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    J. Martinich, “A vertex-closing approach to the p-Center problem,” Naval. Res. Log., 35, 185–201 (1988).MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    J. Plesnik, “A heuristic for the p-Center problem in graphs,” Discr. Appl. Math., 17, 263–268 (1987).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Departamento de Matemática da Universidade de AveiroAveiroPortugal
  2. 2.Centro de Estudos Florestais, Instituto Superior de AgronomiaTechnical University of LisbonLisboaPortugal

Personalised recommendations