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On the Weight-Constrained Minimum Spanning Tree Problem

  • Agostinho Agra
  • Adelaide Cerveira
  • Cristina Requejo
  • Eulália Santos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6701)

Abstract

We consider the weight-constrained minimum spanning tree problem which has important applications in telecommunication networks design. We discuss and compare several formulations. In order to strengthen these formulations, new classes of valid inequalities are introduced. They adapt the well-known cover, extended cover and lifted cover inequalities. They incorporate information from the two subsets: the set of spanning trees and the knapsack set. We report computational experiments where the best performance of a standard optimization package was obtained when using a formulation based on the well-known Miller-Tucker-Zemlin variables combined with separation of cut-set inequalities.

Keywords

Valid Inequality Linear Relaxation Span Tree Problem Weight Constraint Minimum Span Tree Problem 
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.

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References

  1. 1.
    Aggarwal, V., Aneja, Y.P., Nair, K.P.K.: Minimal spanning tree subject to a side constraint. Computers and Operations Research 9, 287–296 (1982)CrossRefGoogle Scholar
  2. 2.
    Gouveia, L.: Using the Miller-Tucker-Zemlin constraints to formulate a minimal spanning tree problem with hop constraints. Computers and Operations Research 22(9), 959–970 (1995)CrossRefzbMATHGoogle Scholar
  3. 3.
    Hassin, R., Levin, A.: An efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection. SIAM Journal on Computing 33(2), 261–268 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hong, S.P., Chung, S.J., Park, B.H.: A fully polynomial bicriteria approximation scheme for the constrained spanning tree problem. Operations Research Letters 32, 233–239 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kaparis, K., Letchford, A.: Separation algorithms for 0-1 knapsack polytopes. Mathematical Programming 124(1–2), 69–91 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Magnanti, T., Wolsey, L.: Optimal trees. In: Ball, M., Magnanti, T., Monma, C., Nemhauser, G. (eds.) Network Models. Handbooks in Operations Research and Management Science, vol. 7, pp. 503–615. Elsevier Science Publishers, North-Holland, Amsterdam (1995)CrossRefGoogle Scholar
  7. 7.
    Miller, C., Tucker, A., Zemlin, R.: Integer programming formulations and travelling salesman problems. Journal of the Association for Computing Machinery 7, 326–329 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Pisinger, D.: Where are the hard knapsack problems? Technical Report 2003/08, DIKU, University of Copenhagen, Denmark (2003)Google Scholar
  9. 9.
    Ravi, R., Goemans, M.: The constrained minimum spanning tree problem. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 66–75. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  10. 10.
    Shogan, A.: Constructing a minimal-cost spanning tree subject to resource constraints and flow requirements. Networks 13, 169–190 (1983)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yamada, T., Watanabe, K., Kataoka, S.: Algorithms to solve the knapsack constrained maximum spanning tree problem. International Journal of Computer Mathematics 82, 23–34 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Agostinho Agra
    • 1
  • Adelaide Cerveira
    • 2
  • Cristina Requejo
    • 1
  • Eulália Santos
    • 3
  1. 1.CIDMA and Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.CIO and Department of MathematicsUniversity of Trás-os-Montes and Alto DouroVila RealPortugal
  3. 3.CIDMA and School of Technology and ManagementPolytechnic Institute of LeiriaLeiriaPortugal

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