Abstract
The minimum dominating set problem (MDSP) aims to construct the minimum-size subset \(D \subset V\) of a graph \(G = (V, E)\) such that every vertex has at least one neighbor in D. The problem is proved to be NP-hard [5]. In a recent industrial application, we encountered a more general variant of MDSP that extends the neighborhood relationship as follows: a vertex is a k-neighbor of another if there exists a linking path through no more than k edges between them. This problem is called the minimum k-dominating set problem (MkDSP) and the dominating set is denoted as \(D_k\). The MkDSP can be used to model applications in social networks [2] and design of wireless sensor networks [3]. In our case, a telecommunication company uses the problem model to supervise a large social network up to 17 millions nodes via a dominating subset in which k is set to 3.
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Nguyen, M.H., Hà, M.H., Hoang, D.T., Nguyen, D.N., Dutkiewicz, E., Tran, T.T. (2019). An Efficient Algorithm for the k-Dominating Set Problem on Very Large-Scale Networks (Extended Abstract). In: Tagarelli, A., Tong, H. (eds) Computational Data and Social Networks. CSoNet 2019. Lecture Notes in Computer Science(), vol 11917. Springer, Cham. https://doi.org/10.1007/978-3-030-34980-6_9
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DOI: https://doi.org/10.1007/978-3-030-34980-6_9
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