Skip to main content
SpringerLink
Log in

An exact and heuristic approach for the d-minimum branch vertices problem

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

Given a connected graph \(G=(V,E)\), the d-Minimum Branch Vertices (d-MBV) problem consists in finding a spanning tree of G with the minimum number of vertices with degree strictly greater than d. We developed a Miller–Tucker–Zemlin based formulation with valid inequalities for this problem. The results obtained for different values of d show the effectiveness of the proposed method, which has solved several instances faster than previous methods. Also, an heuristic is proposed for this problem, that was tested on several instances of the Minimum Branch Vertices problem, which is the d-MBV problem, when \(d = 2\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akgün, İ., Tansel, B.Ç.: Min-degree constrained minimum spanning tree problem: new formulation via Miller–Tucker–Zemlin constraints. Comput. Oper. Res. 37(1), 72–82 (2010)

    Article  MathSciNet  Google Scholar 

  2. Bastos, L., Ochi, L.S., Protti, F., Subramanian, A., Martins, I., Pinheiro, R.G.S.: Efficient algorithms for cluster editing. J. Comb. Optim. 31(1), 347–371 (2016)

    Article  MathSciNet  Google Scholar 

  3. Carrabs, F., Cerulli, R., Gaudioso, M., Gentili, M.: Lower and upper bounds for the spanning tree with minimum branch vertices. Comput. Optim. Appl. 56(2), 405–438 (2013)

    Article  MathSciNet  Google Scholar 

  4. Cerulli, R., Gentili, M., Iossa, A.: Bounded-degree spanning tree problems: models and new algorithms. Comput. Optim. Appl. 42(3), 353–370 (2009)

    Article  MathSciNet  Google Scholar 

  5. Coelho, V.N., Grasas, A., Ramalhinho, H., Coelho, I.M., Souza, M.J.F., Cruz, R.C.: An ILS-based algorithm to solve a large-scale real heterogeneous fleet VRP with multi-trips and docking constraints. Eur. J. Oper. Res. 250(2), 367–376 (2016)

    Article  MathSciNet  Google Scholar 

  6. Gargano, L., Hell, P., Stacho, L., Vaccaro, U.: Spanning trees with bounded number of branch vertices. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol. 2380. Springer, Berlin, Heidelberg (2002)

    Google Scholar 

  7. Landete, M., Marín, A., Sainz-Pardo, J.L.: Decomposition methods based on articulation vertices for degree-dependent spanning tree problems. Comput. Optim. Appl. 68(3), 749–773 (2017)

    Article  MathSciNet  Google Scholar 

  8. Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search: framework and applications. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146. Springer, Boston, MA (2010)

    Chapter  Google Scholar 

  9. Marín, A.: Exact and heuristic solutions for the minimum number of branch vertices spanning tree problem. Eur. J. Oper. Res. 245(3), 680–689 (2015)

    Article  MathSciNet  Google Scholar 

  10. Martinez, L.C., Da Cunha, A.S.: The min-degree constrained minimum spanning tree problem: formulations and branch-and-cut algorithm. Discret. Appl. Math. 163, 210–224 (2014)

    Article  MathSciNet  Google Scholar 

  11. Melo, R.A., Samer, P., Urrutia, S.: An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices. Comput. Optim. Appl. 65(3), 821–844 (2016)

    Article  MathSciNet  Google Scholar 

  12. Merabet, M., Molnar, M.: Generalization of the Minimum Branch Vertices Spanning Tree Problem. PhD thesis, Nanyang Technological University, Singapore (2016)

  13. Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM (JACM) 7(4), 326–329 (1960)

    Article  MathSciNet  Google Scholar 

  14. Schmidt, J.M.: A simple test on 2-vertex-and 2-edge-connectivity. Inf. Process. Lett. 113(7), 241–244 (2013)

    Article  MathSciNet  Google Scholar 

  15. Silva, D.M., Silva, R.M.A., Mateus, G.R., Gonçalves, J.F., Resende, M.G.C., Festa, P.: An iterative refinement algorithm for the minimum branch vertices problem. In: International Symposium on Experimental Algorithms, pp. 421–433. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Silva, R.M.A., Silva, D.M., Mateus, G.R., Gonçalves, J.F., Resende, M.G.C., Festa, P.: An edge-swap heuristic for generating spanning trees with minimum number of branch vertices. Optim. Lett. 8(4), 1225–1243 (2014)

    Article  MathSciNet  Google Scholar 

  17. Silvestri, S., Laporte, G., Cerulli, R.: A branch-and-cut algorithm for the minimum branch vertices spanning tree problem. Comput. Oper. Res. 81, 322–332 (2017)

    Article  MathSciNet  Google Scholar 

  18. Sundar, S., Singh, A., Rossi, A.: New heuristics for two bounded-degree spanning tree problems. Inf. Sci. 195, 226–240 (2015)

    Article  MathSciNet  Google Scholar 

  19. Vilar, J.V., Arroyo, J.E.C.: ILS Heuristics for the single-machine scheduling problem with sequence-dependent family setup times to minimize total tardiness. J. Appl. Math. 1(1), 1–15 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computing, Universidade Federal Fluminense, Rio de Janeiro, Brazil

    Jorge Moreno, Yuri Frota & Simone Martins

Authors
  1. Jorge Moreno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuri Frota
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simone Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge Moreno.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moreno, J., Frota, Y. & Martins, S. An exact and heuristic approach for the d-minimum branch vertices problem. Comput Optim Appl 71, 829–855 (2018). https://doi.org/10.1007/s10589-018-0027-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-018-0027-x

Keywords

Search

Navigation