Theoretical Article
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Calculating the Centrality Values According to the Strengths of Entities Relative to their Neighbours and Designing a New Algorithm for the Solution of the Minimal Dominating Set Problem

Year 2023, , 50 - 56, 08.06.2023
https://doi.org/10.53070/bbd.1295038

Abstract

The dominating set problem in graph theory is an NP-complete problem for an arbitrary graph. There are many approximation-based studies in the literature to solve the dominating set problems for a given graph. Some of them are exact algorithms with exponential time complexities and some of them are based on approximation without robustness with respect to obtained solutions. In this study, the Malatya centrality value was used and a new Malatya centrality value was defined to solve the dominating set problem for a given graph. The improved algorithms have polynomial time and space complexities.

References

  • Bourgeois, N., Croce, F.D., Escoffier, B., Paschos, V.T.,” Fast algorithms for min independent dominating set”, Discrete Applied Mathematics, Vol:161, pp:558-572, 2013.
  • Goddard, W., Henning, M.A.,”Independent domination in graphs: A survey and recent results”, Discrete Mathematics, Vol:313, pp:839-854, 2013.
  • Grandoni, F.,”A note on the complexity of minimum dominating set”, Journal of Discrete Algorithms, Vol:4, pp:209-214, 2006.
  • Guha, S., Khuller, S.,”Approximation Algorithms for Connected Dominating Sets”, Algorithmica, Vol:20, pp:374-387, 1998.
  • Hagerup, T., “A strengthened analysis of an algorithm for Dominating Set in planar graphs”, Discrete Applied Mathematics, Vol:160, pp:793-798, 2012.
  • Karci, A., Yakut, S., Oztemiz, F.,” A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm”, Journal of Computer Science, Vol:7, pp:81-88,2022.
  • Khamis, S.M., Daoud, S.S., Essa, H.A.E,” A randomized algorithm for determining dominating sets in graphs of maximum degree five”, Theoretical Computer Science, Vol:410, pp:5122-5127, 2009.
  • Khuller, S., Yang, S.,” Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm”, Algorithmica, Vol:81, pp:2592-2605, 2019.
  • Van Rooij, J.M.M., Bodlaender, H.L.,” Exact algorithms for dominating set”, Discrete Applied Mathematics, Vol:159, pp:2147-2164, 2011.
  • Wawrzyniak, W.,”A local approximation algorithm for minimum dominating set problem in anonymous planar networks”, Distributed Computing, Vol:28, pp:321-331, 2015.

Calculating the Centrality Values According to the Strengths of Entities Relative to their Neighbours and Designing a New Algorithm for the Solution of the Minimal Dominating Set Problem

Year 2023, , 50 - 56, 08.06.2023
https://doi.org/10.53070/bbd.1295038

Abstract

The dominating set problem in graph theory is an NP-complete problem for an arbitrary graph. There are many approximation-based studies in the literature to solve the dominating set problems for a given graph. Some of them are exact algorithms with exponential time complexities and some of them are based on approximation without robustness with respect to obtained solutions. In this study, the Malatya centrality value was used and a new Malatya centrality value was defined to solve the dominating set problem for a given graph. The improved algorithms have polynomial time and space complexities.

References

  • Bourgeois, N., Croce, F.D., Escoffier, B., Paschos, V.T.,” Fast algorithms for min independent dominating set”, Discrete Applied Mathematics, Vol:161, pp:558-572, 2013.
  • Goddard, W., Henning, M.A.,”Independent domination in graphs: A survey and recent results”, Discrete Mathematics, Vol:313, pp:839-854, 2013.
  • Grandoni, F.,”A note on the complexity of minimum dominating set”, Journal of Discrete Algorithms, Vol:4, pp:209-214, 2006.
  • Guha, S., Khuller, S.,”Approximation Algorithms for Connected Dominating Sets”, Algorithmica, Vol:20, pp:374-387, 1998.
  • Hagerup, T., “A strengthened analysis of an algorithm for Dominating Set in planar graphs”, Discrete Applied Mathematics, Vol:160, pp:793-798, 2012.
  • Karci, A., Yakut, S., Oztemiz, F.,” A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm”, Journal of Computer Science, Vol:7, pp:81-88,2022.
  • Khamis, S.M., Daoud, S.S., Essa, H.A.E,” A randomized algorithm for determining dominating sets in graphs of maximum degree five”, Theoretical Computer Science, Vol:410, pp:5122-5127, 2009.
  • Khuller, S., Yang, S.,” Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm”, Algorithmica, Vol:81, pp:2592-2605, 2019.
  • Van Rooij, J.M.M., Bodlaender, H.L.,” Exact algorithms for dominating set”, Discrete Applied Mathematics, Vol:159, pp:2147-2164, 2011.
  • Wawrzyniak, W.,”A local approximation algorithm for minimum dominating set problem in anonymous planar networks”, Distributed Computing, Vol:28, pp:321-331, 2015.
There are 10 citations in total.

Details

Primary Language English
Subjects Computer Software, Software Testing, Verification and Validation
Journal Section PAPERS
Authors

Şeyda Karcı 0000-0001-8489-7828

Fatih Okumuş 0000-0003-3046-9558

Ali Karci 0000-0002-8489-8617

Early Pub Date June 8, 2023
Publication Date June 8, 2023
Submission Date May 14, 2023
Acceptance Date June 2, 2023
Published in Issue Year 2023

Cite

APA Karcı, Ş., Okumuş, F., & Karci, A. (2023). Calculating the Centrality Values According to the Strengths of Entities Relative to their Neighbours and Designing a New Algorithm for the Solution of the Minimal Dominating Set Problem. Computer Science, Vol:8(Issue:1), 50-56. https://doi.org/10.53070/bbd.1295038

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