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Construct, Merge, Solve and Adapt Applied to the Maximum Disjoint Dominating Sets Problem

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Metaheuristics (MIC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13838))

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Abstract

We propose a “construct, merge, solve and adapt” (CMSA) approach for the maximum disjoint dominating sets problem (MDDSP), which is a complex variant of the classical minimum dominating set problem in undirected graphs. The problem requires to find as many vertex-disjoint dominating sets of a given graph as possible. CMSA is a recent metaheuristic approach based on the idea of problem instance reduction. At each iteration of the algorithm, sub-instances of the original problem instance are solved by an exact solver. These sub-instances are obtained by merging the solution components of probabilistically generated solutions. CMSA is the first metaheuristic proposed for solving the MDDSP. The obtained results show that CMSA outperforms all existing greedy heuristics.

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Notes

  1. 1.

    Remember that DNP stands for “domatic number problem”.

  2. 2.

    Remember that any solution to the MDDSP can be trivially transformed to a solution to the DPP by adding those vertices that do not belong to any of the disjoint dominating sets to one of the dominating sets of the MDDSP-solution.

  3. 3.

    See Sect. 4.1 for the definition of function r().

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Acknowledgments

This research was partially supported by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No 952215. Furthermore, this work was supported by grant PID2019-104156GB-I00 funded by MCIN/AEI/10.13039 /501100011033.

Author information

Authors and Affiliations

  1. DPIA, University of Udine, via delle Scienze 206, 33100, Udine, Italy

    Roberto Maria Rosati

  2. Artificial Intelligence Research Institute (IIIA-CSIC) Campus of the UAB, Bellaterra, Spain

    Roberto Maria Rosati & Christian Blum

  3. Department of Computer Science, Mechatronics Laboratory (LMETR), Ferhat Abbas University, Sétif 1, 19000, Sétif, Algeria

    Salim Bouamama

Authors
  1. Roberto Maria Rosati
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  2. Salim Bouamama
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  3. Christian Blum
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Corresponding author

Correspondence to Roberto Maria Rosati .

Editor information

Editors and Affiliations

  1. University of Udine, Udine, Italy

    Luca Di Gaspero

  2. University of Napoli - Federico II, Napoli, Italy

    Paola Festa

  3. University of Paris Est, Paris, France

    Amir Nakib

  4. University of Catania, Catania, Italy

    Mario Pavone

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Rosati, R.M., Bouamama, S., Blum, C. (2023). Construct, Merge, Solve and Adapt Applied to the Maximum Disjoint Dominating Sets Problem. In: Di Gaspero, L., Festa, P., Nakib, A., Pavone, M. (eds) Metaheuristics. MIC 2022. Lecture Notes in Computer Science, vol 13838. Springer, Cham. https://doi.org/10.1007/978-3-031-26504-4_22

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  • DOI: https://doi.org/10.1007/978-3-031-26504-4_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26503-7

  • Online ISBN: 978-3-031-26504-4

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