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

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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.

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Data availability statement

The datasets analysed during the current study are available in the Social Networks Samples repository, http://davidchalupa.github.io/research/data/social.html.

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Funding

This research was funded by the Group Building Scientific Innovation Project for Universities in Chongqing (CXQT21021); and Joint Training Base Construction Project for Graduate Students in Chongqing (JDLHPYJD2021016).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, China

    Lihe Guan & Hong Wang

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  1. Lihe Guan
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  2. Hong Wang
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Contributions

Methodology, Guan LH; Software, Wang H; Writing—original draft preparation, Guan LH; Writing—review and editing, Guan LH and Wang H. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Lihe Guan.

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Guan, L., Wang, H. A heuristic approximation algorithm of minimum dominating set based on rough set theory. J Comb Optim 44, 752–769 (2022). https://doi.org/10.1007/s10878-021-00834-x

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