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A heuristic approximation algorithm of minimum dominating set based on rough set theory

Author

Listed:
  • Lihe Guan

    (Chongqing Jiaotong University)

  • Hong Wang

    (Chongqing Jiaotong University)

Abstract

The minimum dominating set of graph has been widely used in many fields, but its solution is NP-hard. The complexity and approximation accuracy of existing algorithms need to be improved. In this paper, we introduce rough set theory to solve the dominating set of undirected graph. First, the adjacency matrix of undirected graph is used to establish an induced decision table, and the minimum dominating set of undirected graph is equivalent to the minimum attribute reduction of its induced decision table. Second, based on rough set theory, the significance of attributes (i.e., vertices) based on the approximate quality is defined in induced decision table, and a heuristic approximation algorithm of minimum dominating set is designed by using the significance of attributes (i.e., vertices) as heuristic information. This algorithm uses forward and backward search mechanism, which not only ensures to find a minimal dominating set, but also improves the approximation accuracy of minimum dominating set. In addition, a cumulative strategy is used to calculate the positive region of induced decision table, which effectively reduces the computational complexity. Finally, the experimental results on public datasets show that our algorithm has obvious advantages in running time and approximation accuracy of the minimum dominating set.

Suggested Citation

  • Lihe Guan & Hong Wang, 2022. "A heuristic approximation algorithm of minimum dominating set based on rough set theory," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 752-769, August.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00834-x
    DOI: 10.1007/s10878-021-00834-x
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    References listed on IDEAS

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    1. Fuyu Yuan & Chenxi Li & Xin Gao & Minghao Yin & Yiyuan Wang, 2019. "A Novel Hybrid Algorithm for Minimum Total Dominating Set Problem," Mathematics, MDPI, vol. 7(3), pages 1-11, February.
    2. Thang N. Dinh & Yilin Shen & Dung T. Nguyen & My T. Thai, 2014. "On the approximability of positive influence dominating set in social networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 487-503, April.
    3. Shiping Wang & Qingxin Zhu & William Zhu & Fan Min, 2013. "Equivalent Characterizations of Some Graph Problems by Covering-Based Rough Sets," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
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