An Iterative Refinement Algorithm for the Minimum Branch Vertices Problem

  • Diego M. Silva
  • Ricardo M. A. Silva
  • Geraldo R. Mateus
  • José F. Gonçalves
  • Mauricio G. C. Resende
  • Paola Festa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


This paper presents a new approach to solve the NP-complete minimum branch vertices problem (MBV) introduced by Gargano et. al [1]. In spite of being a recently proposed problem in the network optimization literature, there are some heuristics to solve it [3]. The main contribution of this paper consists in a new heuristic based on the iterative refinement approach proposed by Deo and Kumar [2]. The experimental results suggest that this approach is capable of finding solutions that are better than the best known in the literature. In this work, for instance, the proposed heuristic found better solutions for 78% of the instances tested. The heuristic looks very promising for the solution of problems related with constrained spanning trees.


Constrained spanning trees Branch vertices Iterative refinement 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gargano, L., Hell, P., Stacho, L., Vaccaro, U.: Spanning trees with bounded number of branch vertices. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 355–365. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Deo, N., Kumar, N.: Computation of Constrained Spanning Trees: A Unified Approach. In: Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 450, pp. 194–220. Springer, New York (1997)CrossRefGoogle Scholar
  3. 3.
    Cerulli, R., Gentili, M., Iossa, A.: Bounded-Degree Spanning Tree Problems: Models and New Algorithms. Comput. Optim. Appl. 42, 353–370 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boldon, B., Deo, N., Kumar, N.: Minimum-Weight Degree-Constrained Spanning Tree Problem: Heuristics and Implementation on an SIMD Parallel Machine. Technical Report CS-TR-95-02, Department of Computer Science, University of Central Florida, Orlando, FL (1995)Google Scholar
  5. 5.
    Mao, L.J., Deo, N., Lang, S.D.: A Comparison of Two Parallel Approximate Algorithms for the Degree-Constrained Minimum Spanning Tree Problem. Congressus Numerantium 123, 15–32 (1997)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Abdalla, A., Deo, N., Gupta, P.: Random-Tree Diameter and the Diameter Constrained MST. Congressus Numerantium 144, 161–182 (2000)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn., pp. 498–509. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications, pp. 521–522. Prentice-Hall, Englewood Cliffs (1993)zbMATHGoogle Scholar
  9. 9.
    Klingman, D., Napier, A., Stutz, J.: NETGEN – A program for generating large scale (un)capacitated assignment, transportation, and minimum cost flow network problems. Managent Science 20, 814–821 (1974)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Diego M. Silva
    • 1
    • 2
  • Ricardo M. A. Silva
    • 1
    • 3
  • Geraldo R. Mateus
    • 2
  • José F. Gonçalves
    • 4
  • Mauricio G. C. Resende
    • 5
  • Paola Festa
    • 6
  1. 1.Dept. of Computer ScienceFederal University of LavrasLavrasBrazil
  2. 2.Dept. of Computer ScienceFederal University of Minas GeraisBelo HorizonteBrazil
  3. 3.Center of InformaticsFederal University of PernambucoRecifeBrazil
  4. 4.LIAAD, Faculdade de Economia do PortoPortoPortugal
  5. 5.AT&T Labs ResearchInternet and Network Systems ResearchFlorham ParkUSA
  6. 6.Dept. of Mathematics and Applications ‘‘R. Caccioppoli’’University of Napoli FEDERICO IINapoliItaly

Personalised recommendations