On construction of quality virtual backbone in wireless networks using cooperative communication

An extended connected dominating set (ECDS) in a wireless network with cooperative communication (CC) is a subset of nodes such that its induced subgraph is connected and each node outside the ECDS is covered by either one neighbor or several quasineighbors in the ECDS. Traditionality, the size of virtual backbone (VB) is the only factor considered in the problem of CDS construction. However, diameter is also an important factor to evaluate VB. In this paper we consider the problem of constructing quality ECDSs in unit disk graphs under CC with both of these two factors. We propose a two-phase centralized algorithm BD-ECDS to construct an ECDS for a given UDG with CC, which has a constant performance ratio (PR) and diameter. To obtain the PR of this two-phase centralized algorithm, we first give an upper bound of the EDS and use this upper bound to prove that the size of the ECDS under CC generated by the centralized algorithm is no greater than $120\left|ECD{S}_{opt}\right|-2$, where $ECD{S}_{opt}$ is the size of the minimum ECDS. Furthermore, our theoretical analysis and simulation results show that our algorithm BD-ECDS is superior to previous approaches.