Skip to main content

Advertisement

SpringerLink
Log in

A hybrid heuristic for dominating tree problem

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Given an undirected, connected, edge-weighted graph, the dominating tree problem (DTP) seeks on this graph a tree of minimum weight such that each node of the graph either belongs to the tree or is adjacent to a node in the tree. This problem is \({\fancyscript{NP}}\)-hard. In this paper, we present an evolutionary algorithm with guided mutation (EA/G) to solve the DTP. This problem has several practical applications in the field of wireless sensor networks. EA/G is a recently proposed evolutionary algorithm that tries to overcome the shortcomings of genetic algorithms (GAs) and estimation of distribution algorithms both, and has the characteristics of both. We have compared the performance of our proposed approach with the state-of-the-art approaches presented in the literature. Computational results show the superiority of our approach in terms of solution quality as well as execution time.

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
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Arkin EM, Halldórsson MM, Hassin R (1993) Approximating the tree and tour covers of a graph. Inf Process Lett 47:275–282

    Article  MATH  Google Scholar 

  • Fujito T (2001) On approximability of the independent/connected edge dominating set problems. Inf Process Lett 79:261–266

  • Fujito T (2006) How to trim an mst: a 2-approximation algorithm for minimum cost tree cover. In: Bugliesi M, Preneel B, Sassone V, Wegener I (eds) Automata, languages and programming, Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg, pp 431–442

  • Guha S, Khuller S (1998) Approximation algorithms for connected dominating sets. Algorithmica 20(4):374–387

    Article  MathSciNet  MATH  Google Scholar 

  • Park MA, Willson J, Wang C, Thai M, Wu W, Farago A (2007) A dominating and absorbent set in a wireless ad-hoc network with different transmission ranges. In: Proceedings of the 8th ACM international symposium on mobile ad hoc networking and computing, MobiHoc ’07. ACM, New York, pp 22–31

  • Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36:1389–1401

    Article  Google Scholar 

  • Raidl G, Julstrom B (2003) Edge-sets: an effective evolutionary coding of spanning trees. IEEE Trans Evolut Comput 7:225–239

    Article  Google Scholar 

  • Shin I, Shen Y, Thai MT (2010) On approximation of dominating tree in wireless sensor networks. Optim Lett 4(3):393–403

    Article  MathSciNet  MATH  Google Scholar 

  • Sundar S, Singh A (2013) New heuristic approaches for the dominating tree problem. Appl Soft Comput 13(12):4695–4703

    Article  Google Scholar 

  • Thai MT, Wang F, Liu D, Zhu S, Du D-Z (2007) Connected dominating sets in wireless networks with different transmission ranges. IEEE Trans Mobile Comput 6(7):721–730

    Article  Google Scholar 

  • Thaiand MT, Tiwari R, Du D-Z (2008) On construction of virtual backbone in wireless ad hoc networks with unidirectional links. IEEE Trans Mobile Comput 7(9):1098–1109

    Article  Google Scholar 

  • Wan P-J, Alzoubi KM, Frieder O (2002) Distributed construction of connected dominating set in wireless ad hoc networks. In: Proceedings of the twenty-first annual joint conference of the IEEE Computer and Communications Societies (INFOCOM 2002), vol 3, pp 1597–1604

  • Wu J, Hailan L (1999) On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of the 3rd international workshop on discrete algorithms and methods for mobile computing and communications, DIALM ’99. ACM, New York, pp 7–14

  • Zhang N, Shin I, Li B, Boyaci C, Tiwari R, Thaiand MT (2008) New approximation for minimum-weight routing backbone in wireless sensor network. Wireless algorithms, systems, and applications, Lecture Notes in Computer Science, vol 5258. Springer, Berlin, Heidelberg, pp 96–108

  • Zhang Q, Sun J, Tsang E (2005) An evolutionary algorithm with guided mutation for the maximum clique problem. IEEE Trans Evolut Comput 9:192–200

    Article  Google Scholar 

Download references

Acknowledgments

Authors are grateful to two anonymous reviewers for their valuable comments and suggestions which has helped in improving the quality of this paper.

Author information

Authors and Affiliations

  1. School of Computer and Information Sciences, University of Hyderabad, Hyderabad, 500046, India

    Sachchida Nand Chaurasia & Alok Singh

Authors
  1. Sachchida Nand Chaurasia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alok Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alok Singh.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chaurasia, S.N., Singh, A. A hybrid heuristic for dominating tree problem. Soft Comput 20, 377–397 (2016). https://doi.org/10.1007/s00500-014-1513-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1513-4

Keywords

Search

Navigation