Constructing d-Robust Connected Dominating Sets in Wireless Sensor Networks With Unstable Transmission Ranges

Abstract

A connected dominating set (CDS) can act as a virtual backbone (VB) in a wireless sensor network (WSN). The overhead in a WSN is usually determined by the size of the corresponding VB. However, the construction of minimum CDSs (MCDSs) has been proven to be an NP-hard problem. Thus, most researchers use approximation algorithms to find smaller CDSs. In certain applications, the transmission radii of some nodes in the network are unstable due to certain environmental factors such as obstacles, signal interference and node movement. Thus, the robustness of VBs in WSNs should be considered. In this paper, we propose the concept of a $d $ -robust CDS and corresponding algorithms to construct $d $ -robust CDSs in WSNs with unstable transmission ranges. We propose algorithms for a $d $ -robust CDS that is bounded by $[{40.68/(1-d)^{2}+10.17}]\cdot opt+[{31.32/(1-d)^{2}+7.83}] $ , where $opt $ is the size of the MCDS and $d \in [0,1$ ). Through simulations, we show the relationship between the size of the $d$ -robust CDS and the value of $d$ and compare our algorithms with existing algorithms in terms of the robustness degree of the CDS. The results show that the CDSs produced by our algorithms exhibit better robustness.