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A novel local search approach with connected dominating degree-based incremental neighborhood evaluation for the minimum 2-connected dominating set problem

Author

Listed:
  • Mao Luo

    (Hubei University of Technology)

  • Huigang Qin

    (Hubei University of Technology)

  • Xinyun Wu

    (Hubei University of Technology)

  • Caiquan Xiong

    (Hubei University of Technology)

Abstract

The minimum connected dominating set problem is widely studied due to its applicability to mobile ad-hoc networks and sensor grids. Its variant the minimum 2-connected dominating set (M-2CDS) problem has become increasingly important because its critical role in designing fault-tolerant network. This paper presents a connected dominating degree-based local search (CDD-LS) tailored for solving the M-2CDS. The proposed algorithm implements an improved swap-based neighborhood structure as well as the corresponding fast neighborhood evaluation method using connected dominating degree data structure. The diversification techniques including tabu strategy and perturbaistion help the search jump out of the local optima improving the efficiency. This study investigates the performance of the CDD-LS algorithm on 38 publicly available benchmark datasets. The results demonstrate that the CDD-LS algorithm significantly improves the best runtime in 19 instances, while providing the equivalent performance in 8 instances. Furthermore, the CDD-LS is tested on 18 newly generated instances to check its capability on large-scale scenarios. To gain a deeper understanding of the algorithm’s effectiveness, an investigation into the key components of the CDD-LS algorithm is conducted.

Suggested Citation

  • Mao Luo & Huigang Qin & Xinyun Wu & Caiquan Xiong, 2024. "A novel local search approach with connected dominating degree-based incremental neighborhood evaluation for the minimum 2-connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-26, July.
    • Handle: RePEc:spr:jcomop:v:47:y:2024:i:5:d:10.1007_s10878-024-01175-1
    DOI: 10.1007/s10878-024-01175-1
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    References listed on IDEAS

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    1. Abilio Lucena & Nelson Maculan & Luidi Simonetti, 2010. "Reformulations and solution algorithms for the maximum leaf spanning tree problem," Computational Management Science, Springer, vol. 7(3), pages 289-311, July.
    2. Yishuo Shi & Yaping Zhang & Zhao Zhang & Weili Wu, 2016. "A greedy algorithm for the minimum $$2$$ 2 -connected $$m$$ m -fold dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 136-151, January.
    3. Austin Buchanan & Je Sang Sung & Sergiy Butenko & Eduardo L. Pasiliao, 2015. "An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 178-188, February.
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