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Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems

Author

Listed:
  • Ruizhi Li

    (School of Computer Science and Technology, Jilin University, Changchun 130012, China
    School of Management Science and Information Engineering, Jilin University of Finance and Economics, Changchun 130117, China)

  • Shuli Hu

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China)

  • Huan Liu

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China)

  • Ruiting Li

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China)

  • Dantong Ouyang

    (School of Computer Science and Technology, Jilin University, Changchun 130012, China)

  • Minghao Yin

    (School of Computer Science and Information Technology, Northeast Normal University, Changchun 130024, China)

Abstract

The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks. In this paper, we propose a novel multi-start local search algorithm (MSLS) to tackle the minimum connected dominating set problem. Firstly, we present the fitness mechanism to design the vertex score mechanism so that our algorithm can jump out of the local optimum. Secondly, we use the configuration checking (CC) mechanism to avoid the cycling problem. Then, we propose the vertex flipping mechanism to change the vertex state by combing the CC mechanism with the vertex score mechanism. Finally, we propose a multi-start local search framework based on these mechanisms. We compare the algorithm MSLS with other compared algorithms on extensive instances. The results of experiment show that MSLS is superior to other algorithms in solution quality and time efficiency on most instances.

Suggested Citation

  • Ruizhi Li & Shuli Hu & Huan Liu & Ruiting Li & Dantong Ouyang & Minghao Yin, 2019. "Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1173-:d:293555
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    References listed on IDEAS

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    1. Bernard Gendron & Abilio Lucena & Alexandre Salles da Cunha & Luidi Simonetti, 2014. "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 645-657, November.
    2. Kelleher, Laura L. & Cozzens, Margaret B., 1988. "Dominating sets in social network graphs," Mathematical Social Sciences, Elsevier, vol. 16(3), pages 267-279, December.
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    Cited by:

    1. Xinyun Wu & Zhipeng Lü & Fred Glover, 2022. "A Fast Vertex Weighting-Based Local Search for Finding Minimum Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 817-833, March.

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