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An adaptive focal distance tabu search approach for the minimum 2-connected dominating set problem

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Abstract

The minimum connected dominating set problem has garnered significant attention due to its wide applications in mobile ad hoc networks and sensor grids. As its variant, the minimum 2-connected dominating set (M-2CDS) problem plays a crucial role in fault-tolerant network design, with its importance increasingly prominent. To address the M-2CDS problem, this paper proposes an adaptive focal distance tabu search algorithm (AFD-TS). The algorithm employs a swap-based neighborhood structure paired with an efficient neighborhood evaluation method, enhanced by adaptive tabu strategies. It also incorporates several adaptive techniques, such as innovative diversification mechanisms, traceback strategies, and reverse approaches, all organized within a unique solution pool structure. To improve the efficiency, the algorithm applies two different optimization strategies and a fast maintenance for the set of cut vertices. Experiments were conducted on 37 public benchmark datasets. Results indicate that AFD-TS significantly reduced the running time in 12 instances while maintaining comparable performance in 15 ones. To verify the algorithm’s solving capability in large-scale complex scenarios, tests were further conducted on 34 newly generated instances. Experimental results demonstrate that the AFD-TS algorithm achieved leading performance across all new instances, fully proving its superiority in handling complex problems. Furthermore, this study conducted an analysis of the key components of the AFD-TS algorithm, comprehensively assessing the contribution of each module to the overall effectiveness of the algorithm, providing important basis for further optimization and improvement.

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Data Availability

The large-scale dataset and the source code and executable files of the proposed algorithm have been made public at https://github.com/Yinwanglau/BD_BP_BA-DATASETS.

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Funding

The research was supported by the National Natural Science Foundation of China (Grant Nos. 62402164 and 62472149).

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Authors and Affiliations

  1. School of Computer Science, Hubei University of Technology, Wuhan, 430068, China

    Mao Luo, Xianhong Liu, Xinyun Wu, Caiquan Xiong & Yuanzhi Ke

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  1. Mao Luo
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  2. Xianhong Liu
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  3. Xinyun Wu
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Correspondence to Xinyun Wu.

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Luo, M., Liu, X., Wu, X. et al. An adaptive focal distance tabu search approach for the minimum 2-connected dominating set problem. J Supercomput 81, 501 (2025). https://doi.org/10.1007/s11227-025-07014-2

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  • DOI: https://doi.org/10.1007/s11227-025-07014-2

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