Skip to main content
SpringerLink
Log in

Parallel strategic oscillation: an application to the maximum leaf spanning tree problem

  • Regular Paper
  • Published:
Progress in Artificial Intelligence Aims and scope Submit manuscript

Abstract

The maximum leaf spanning tree problem consists in finding a spanning tree of a graph that maximizes the number of leaves that the tree has. This problem has been found to be \(\mathcal {NP}\)-hard for general graphs. It has several relevant applications in the context of telecommunication networks. In this paper, we tackle this problem by proposing the use of a parallel algorithm based on the strategic oscillation methodology. In particular, we propose two different parallel approaches and we compare our best variant with previous algorithms of the state of the art. The proposed approach outperforms previous ones in the state of the art, which is also confirmed by the use of statistical tests.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. http://math.nist.gov/MatrixMarket/data/Harwell-Boeing/.

References

  1. Alba, E.: Parallel Metaheuristics: A New Class of Algorithms, vol. 47. Wiley, New York (2005)

    Book  MATH  Google Scholar 

  2. Balasundaram, B., Butenko, S.: Graph domination, coloring and cliques in telecommunications. In: Handbook of Optimization in Telecommunications, pp. 865–890. Springer, New York (2006)

  3. Chen, S., Ljubić, I., Raghavan, S.: The regenerator location problem. Networks 55, 205–220 (2010)

    MathSciNet  MATH  Google Scholar 

  4. Chen, S., Raghavan, S.: The regenerator location problem. In: Proceedings of the 2007 International Network Optimization Conference (INOC’07) (2007)

  5. Cook, S.: CUDA Programming: A Developer’s Guide to Parallel Computing with GPUs (Applications of GPU Computing), 1st edn. Morgan Kaufmann Publishers Inc., San Francisco (2012)

    Google Scholar 

  6. Duarte, A., Martí, R., Gortázar, F.: Path relinking for large-scale global optimization. Soft Comput. 15, 2257–2273 (2011)

    Article  Google Scholar 

  7. Duarte, A., Martí, R., Resende, M., Silva, R.: Improved heuristics for the regenerator location problem. Int. Trans. Oper. Res. 21, 541–558 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Duarte, A., Pantrigo, J.J., Pardo, E.G., Sánchez-Oro, J.: Parallel variable neighbourhood search strategies for the cutwidth minimization problem. IMA J. Manag. Math. 27, 55–73 (2016)

  9. Fernandes, L.M., Gouveia, L.: Minimal spanning trees with a constraint on the number of leaves. Eur. J. Oper. Res. 104, 250–261 (1998)

    Article  MATH  Google Scholar 

  10. Fernau, H., Kneis, J., Kratsch, D., Langer, A., Liedloff, M., Raible, D., Rossmanith, P.: An exact algorithm for the maximum leaf spanning tree problem. In: Parameterized and Exact Computation, pp. 161–172. Springer, New York (2009)

  11. Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc. 32, 675–701 (1937)

    Article  MATH  Google Scholar 

  12. Fujie, T.: An exact algorithm for the maximum leaf spanning tree problem. Comput. Oper. Res. 30, 1931–1944 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fujie, T.: The maximum-leaf spanning tree problem: formulations and facets. Networks 43, 212–223 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gao, G., Sato, M., Ayguadé, E.: Special issue on parallel programming with openmp. International Journal of Parallel Programming 36, (2008)

  15. García-López, F., Melián-Batista, B., Moreno-Pérez, J., Moreno-Vega, J.: The parallel variable neighborhood search for the \(p\)-median problem. J. Heuristics 8, 375–388 (2002)

    Article  MATH  Google Scholar 

  16. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  17. Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8, 156–166 (1977)

    Article  Google Scholar 

  18. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Norwell (1997)

    Book  MATH  Google Scholar 

  19. Gortázar, F., Duarte, A., Laguna, M., Martí, R.: Black box scatter search for general classes of binary optimization problems. Comput. Oper. Res. 37, 1977–1986 (2010)

    Article  MATH  Google Scholar 

  20. Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20, 374–387 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Laguna, M., Gortázar, F., Gallego, M., Duarte, A., Martí, R.: A black-box scatter search for optimization problems with integer variables. J. Glob. Optim. 58, 497–516 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lu, H.I., Ravi, R.: Approximating maximum leaf spanning trees in almost linear time. J. Algorithms 29, 132–141 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Oaks, S., Wong, H.: Java Threads. O’Reilly Media (2004)

  25. Sánchez-Oro, J., Duarte, A.: Beyond Unfeasibility: Strategic Oscillation for the Maximum Leaf Spanning Tree Problem. In: Lecture Notes in Computer Science, vol. 9422. Springer, New York (2015)

  26. Sánchez-Oro, J., Sevaux, M., Rossi, A., Martí, R., Duarte, A.: Solving dynamic memory allocation problems in embedded systems with parallel variable neighborhood search strategies. Electron. Notes Discret. Math. 47, 85–92 (2015)

    Article  Google Scholar 

  27. Solis-Oba, R.: 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves. Springer, New York (1998)

    Book  MATH  Google Scholar 

  28. Storer, J.A.: Constructing full spanning trees for cubic graphs. Inf. Process. Lett. 13, 8–11 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  29. Talbi, E.G.: Metaheuristics: from design to implementation. Wiley, New York (2009)

    Book  MATH  Google Scholar 

  30. Wilcoxon, F.: Individual comparisons by ranking methods. Biom. Bull. 1(6)80–83 (1945)

Download references

Acknowledgments

This research has been partially supported by the Spanish “Ministerio de Economía y Competitividad”, and by “Comunidad de Madrid” with Grants Refs. TIN2012-35632-C02 and S2013/ICE-2894, respectively.

Author information

Authors and Affiliations

  1. Dpto. Informática y Estadística, Universidad Rey Juan Carlos, Madrid, Spain

    Jesús Sánchez-Oro, Borja Menéndez & Abraham Duarte

  2. Dpto. Sistemas Informáticos, Universidad Politécnica de Madrid, Madrid, Spain

    Eduardo G. Pardo

Authors
  1. Jesús Sánchez-Oro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Borja Menéndez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eduardo G. Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abraham Duarte
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abraham Duarte.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sánchez-Oro, J., Menéndez, B., Pardo, E.G. et al. Parallel strategic oscillation: an application to the maximum leaf spanning tree problem. Prog Artif Intell 5, 121–128 (2016). https://doi.org/10.1007/s13748-015-0076-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13748-015-0076-7

Keywords

Search

Navigation