Advertisement

An Ant Colony Optimization Approach for the Dominating Tree Problem

  • Shyam Sundar
  • Sachchida Nand Chaurasia
  • Alok SinghEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9873)

Abstract

Dominating tree problem (DTP) seeks a tree DT with minimum total edge weight on a given edge-weighted, connected, and undirected graph so that each vertex of the graph is either a member of DT or adjacent to at least one of the vertices in DT. It is a \(\mathcal {NP}\)-Hard problem and finds its root in providing virtual backbone for routing in wireless sensor networks. For this problem, this paper proposes an ant colony optimization (DT-ACO) approach which is different from an existing ant colony optimization (ACO) approach for the DTP. The differences lie in new strategies for two components, viz. solution construction and update of pheromone trails. These new strategies help DT-ACO in exploring high quality solutions in much lesser time in comparison to existing ACO approach as well as another swarm-based metaheuristic approach for the DTP in the literature. Computational results show that DT-ACO outperforms these two swarm-based approaches in terms of solution quality and execution time both.

Keywords

Dominating tree problem Combinatorial optimization Ant Colony Optimization Heuristic Swarm intelligence 

References

  1. 1.
    Shin, I., Shen, Y., Thai, M.T.: On approximation of dominating tree in wireless sensor networks. Optim. Lett. 4, 393–403 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Zhang, N., Shin, I., Li, B., Boyaci, C., Tiwari, R., Thai, M.T.: New approximation for minimum-weight routing backbone in wireless sensor network. In: Li, Y., Huynh, D.T., Das, S.K., Du, D.-Z. (eds.) WASA 2008. LNCS, vol. 5258, pp. 96–108. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88582-5_12 CrossRefGoogle Scholar
  3. 3.
    Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20, 374–387 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Park, M., Wang, C., Willson, J., Thai, M.T., Wu, W., Farago, A.: A dominating and absorbent set in wireless ad-hoc networks with different transmission range. In: Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC) (2007)Google Scholar
  5. 5.
    Thai, M.T., Tiwari, R., Du, D.-Z.: On construction of virtual backbone in wireless ad hoc networks with unidirectional links. IEEE Trans. Mob. Comput. 7, 1–12 (2008)CrossRefGoogle Scholar
  6. 6.
    Thai, M.T., Wang, F., Liu, D., Zhu, S., Du, D.-Z.: Connected dominating sets in wireless networks with different transmission ranges. IEEE Trans. Mob. Comput. 6, 721–730 (2007)CrossRefGoogle Scholar
  7. 7.
    Wan, P.J., Alzoubi, K.M., Frieder, O.: Distributed construction on connected dominating set in wireless ad hoc networks. In: Proceedings of the Conference of the IEEE Communications Society (INFOCOM) (2002)Google Scholar
  8. 8.
    Chaurasia, S.N., Singh, A.: A hybrid heuristic for dominating tree problem. Soft Comput. 20, 377–397 (2016)CrossRefGoogle Scholar
  9. 9.
    Sundar, S.: A steady-state genetic algorithm for the dominating tree problem. In: Dick, G., et al. (eds.) SEAL 2014. LNCS, vol. 8886, pp. 48–57. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-13563-2_5 Google Scholar
  10. 10.
    Sundar, S., Singh, A.: New heuristic approaches for the dominating tree problem. Appl. Soft Comput. 13, 4695–4703 (2013)CrossRefGoogle Scholar
  11. 11.
    Dorigo, M., Maniezzo, V., Colorni, A.: Positive feedback as a search strategy, Technical Report 91-016. Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy (1991)Google Scholar
  12. 12.
    Dorigo, M.: Optimization, learning and natural algorithms. Ph.D. thesis. Dipartimento di Elettronica, Politecnico di Milano, Italy (1992). [in Italian]Google Scholar
  13. 13.
    Colorni, A., Dorigo, M., Maniezzo, V.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  14. 14.
    Gambardella, L.M., Dorigo, M.: Ant colonies for the traveling salesman problem. BioSyst. 43, 7381 (1997)Google Scholar
  15. 15.
    Gambardella, L.M., Dorigo, M.: A cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1, 5366 (1997)Google Scholar
  16. 16.
    Stützle, T., Hoos, H.H.: Improving the ant system: a detailed report on the \({\cal{MAX-MIN}}\) ant system, Technical report AIDA-96-12, FG Intellektik, FB Informatic, TU Darmstadt, Germany (1996)Google Scholar
  17. 17.
    Stützle, T., Hoos, H.H.: \({\cal{MAX-MIN}}\) ant system. Future Gener. Comput. Syst. 16, 889–914 (2000)Google Scholar
  18. 18.
    Sundar, S., Singh, A.: New heuristics for two bounded-degree spanning tree problems. Inf. Sci. 195, 226–240 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)zbMATHGoogle Scholar
  20. 20.
    Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36, 1389–1401 (1957)CrossRefGoogle Scholar
  21. 21.
    Stützle, T., Hoos, H.H.: New heuristic approaches for the dominating tree problem. Future Gener. Comput. Syst. 16, 889–914 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Shyam Sundar
    • 1
  • Sachchida Nand Chaurasia
    • 2
  • Alok Singh
    • 2
    Email author
  1. 1.Department of Computer ApplicationsNational Institute of Technology RaipurRaipurIndia
  2. 2.School of Computer and Information SciencesUniversity of HyderabadHyderabadIndia

Personalised recommendations