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Finding the minimum k-weighted dominating sets using heuristic algorithms

Author

Listed:
  • Barrena, E.
  • Bermudo, S.
  • Hernández-Díaz, A.G.
  • López-Sánchez, A.D.
  • Zamudio, J.A.

Abstract

In this work, we propose, analyze, and solve a generalization of the k-dominating set problem in a graph, when we consider a weighted graph. Given a graph with weights in its edges, a set of vertices is a k-weighted dominating set if for every vertex outside the set, the sum of the weights from it to its adjacent vertices in the set is bigger than or equal to k. The k-weighted domination number is the minimum cardinality among all k-weighted dominating sets. Since the problem of finding the k-weighted domination number is NP-hard, we have proposed several problem-adapted construction and reconstruction techniques and embedded them in an Iterated Greedy algorithm. The resulting sixteen variants of the Iterated Greedy algorithm have been compared with an exact algorithm. Computational results show that the proposal is able to find optimal or near-optimal solutions within a short computational time. To the best of our knowledge, the k-weighted dominating set problem has never been studied before in the literature and, therefore, there is no other state-of-the-art algorithm to solve it. We have also included a comparison with a particular case of our problem, the minimum dominating set problem and, on average, we achieve same quality results within around 50% of computation time.

Suggested Citation

  • Barrena, E. & Bermudo, S. & Hernández-Díaz, A.G. & López-Sánchez, A.D. & Zamudio, J.A., 2025. "Finding the minimum k-weighted dominating sets using heuristic algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 485-497.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:485-497
    DOI: 10.1016/j.matcom.2024.09.010
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    References listed on IDEAS

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    1. Casado, A. & Bermudo, S. & López-Sánchez, A.D. & Sánchez-Oro, J., 2023. "An iterated greedy algorithm for finding the minimum dominating set in graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 41-58.
    2. Georgie D. M. Hyde, 1988. "South Korea," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-10039-2, December.
    3. Ruiz, Ruben & Stutzle, Thomas, 2007. "A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 2033-2049, March.
    4. Donald A. R. George, 1988. "Kuhn-Tucker theory," Palgrave Macmillan Books, in: Mathematical Modelling for Economists, chapter 3, pages 35-48, Palgrave Macmillan.
    5. Georgie D. M. Hyde, 1988. "Postscript: South Korea 1987," Palgrave Macmillan Books, in: South Korea, pages 221-225, Palgrave Macmillan.
    6. J. N. Hooker & R. S. Garfinkel & C. K. Chen, 1991. "Finite Dominating Sets for Network Location Problems," Operations Research, INFORMS, vol. 39(1), pages 100-118, February.
    7. Wyatt J. Desormeaux & Teresa W. Haynes & Michael A. Henning, 2013. "Edge lifting and total domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 47-59, January.
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