An Efficient Algorithm for the k-Dominating Set Problem on Very Large-Scale Networks (Extended 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 . 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  and design of wireless sensor networks . 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.
- 2.Campan, A., Truta, T.M., Beckerich, M.: Approximation algorithms for \(d\)-hop dominating set problem. In: 12th International Conference on Data Mining, p. 86 (2016)Google Scholar
- 4.Ryan, A.R., Nesreen, K.A.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015)Google Scholar
- 5.Wang, Y., Cai, S., Chen, J., Yin, M.: A fast local search algorithm for minimum weight dominating set problem on massive graphs. In: IJCAI 2018, pp. 1514–1522 (2018)Google Scholar