Skip to main content
SpringerLink
Log in

Computing the Metric Dimension of Hypercube Graphs by Particle Swarm Optimization Algorithms

  • Conference paper
  • First Online:
Recent Advances on Soft Computing and Data Mining (SCDM 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 549))

Included in the following conference series:

Abstract

In this paper, we present a PSO (Particle Swarm Optimization) algorithm for determining the metric dimension of graphs. We choose PSO because of its simplicity, robustness, and adaptability for various optimization problems [5]. Our PSO uses the binary valued vector for particles. The binary valued vector is used to represent which one of vertices of a graph is belong to resolving set. The feasibility is enforced by repairing particles. We tested our PSO by computing the metric dimension of hypercube graphs. The result is our PSO can achieve metric dimension known in literature [8] in reasonable amount of time.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Adiwijaya, Salman, A.N.M., Serra, O., Suprijanto, D., Baskoro, E.T.: Some graphs in \(c_f2\) based on \(f\)-coloring. Int. J. Pure Appl. Math. 102(2), 201–207 (2015)

    Google Scholar 

  2. Beerliova, Z., Eberhard, F., Erlebach, T., Hall, A., Hoffmann, M., Mihal’ak, M., Ram, L.S.: Network discovery and verification. IEEE J. Sel. Areas Commun. 24(12), 2168–2181 (2006)

    Article  MATH  Google Scholar 

  3. Cáceres, J., Hernando, C., Mora, M., Pelayo, I.M., Puertas, M.L., Seara, C., Wood, D.R.: On the metric dimension of Cartesian products of graphs. SIAM J. Discrete Math. 21(2), 423–441 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Harary, F., Melter, R.: On the metric dimension of a graph. Ars Combin. 2(191–195), 1 (1976)

    MATH  Google Scholar 

  5. Ilaya, O., Bil, C., Evans, M.: A particle swarm optimisation approach to graph permutations. In: Information, Decision and Control, IDC 2007, pp. 366–371. IEEE (2007)

    Google Scholar 

  6. Johnson, D.S.: The NP-completeness column: an ongoing guide. J. Algorithms 6(3), 434–451 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in graphs. Discrete Appl. Math. 70(3), 217–229 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kratica, J., Kovačević-Vujčić, V., Čangalović, M.: Computing the metric dimension of graphs by genetic algorithms. Comput. Optim. Appl. 44(2), 343–361 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, K., Abu-Ghazaleh, N.: Virtual coordinates with backtracking for void traversal in geographic routing. In: Kunz, T., Ravi, S.S. (eds.) Ad-Hoc, Mobile, and Wireless Networks. LNCS, vol. 4104, pp. 46–59. Springer, Heidelberg (2006). doi:10.1007/11814764_6

    Chapter  Google Scholar 

  10. Wang, L., Wang, X., Fu, J., Zhen, L.: A novel probability binary particle swarm optimization algorithm and its application. J. Softw. 3(9), 28–35 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing, Telkom University, Jl. Telekomunikasi, Bandung, Indonesia

    Danang Triantoro Murdiansyah &  Adiwijaya

Authors
  1. Danang Triantoro Murdiansyah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adiwijaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Danang Triantoro Murdiansyah .

Editor information

Editors and Affiliations

  1. Department of Information System, University of Malaya, Kuala Lumpur, Malaysia

    Tutut Herawan

  2. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Rozaida Ghazali

  3. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Nazri Mohd Nawi

  4. Universiti Tun Hussein Onn Malaysia, Batu Pahat, Malaysia

    Mustafa Mat Deris

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Murdiansyah, D.T., Adiwijaya (2017). Computing the Metric Dimension of Hypercube Graphs by Particle Swarm Optimization Algorithms. In: Herawan, T., Ghazali, R., Nawi, N.M., Deris, M.M. (eds) Recent Advances on Soft Computing and Data Mining. SCDM 2016. Advances in Intelligent Systems and Computing, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-51281-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-51281-5_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51279-2

  • Online ISBN: 978-3-319-51281-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation