Nguyen, Minh Hai and Ha, Minh Hoang and Dinh, Thai Hoang and Diep, Nguyen and Dutkiewicz, Eryk and Tran, The Trung
(2019)
An Efficient Algorithm for the kDominating Set Problem on Very LargeScale Networks.
In: CSoNet 2019, Ho Chi Minh.
Abstract
The minimum dominating set problem (MDSP) aims to construct the minimumsize subset D⊂V of a graph G=(V,E) such that every vertex has at least one neighbor in D. The problem is proved to be NPhard [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 kneighbor of another if there exists a linking path through no more than k edges between them. This problem is called the minimum kdominating 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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