Discrete beeping is an extremely rigorous local broadcast model depending only on carrier sensing. It describes an anonymous broadcast network where the nodes do not need unique identifiers and have no knowledge about the topology and size of the network. Within such a model, time is divided into slots, and nodes can either beep or keep silent at each slot. We consider the problem of constructing a minimum dominating set (MDS) and a minimum connected dominating set (MCDS), respectively, under the discrete beeping model in this paper.

By assuming that an upper bound N of the network size is known, we first propose and analyze a distributed synchronous algorithm termed BMDS for constructing a minimum dominating set (MDS) and then propose a distributed synchronous algorithm BCDS for CDS construction based on a maximal independent set (MIS) algorithm and a weakly CDS (WCDS). To our best knowledge, we are the first to study the MCDS construction under the discrete beeping model. We prove that the time complexity of BMDS is O(log^{2} N) rounds with constant approximation ratio of at most 2, and BCDS can converge to a CDS within O(log^{3} N) rounds.