A Binary Search Algorithm to Determine the Minimum Transmission Range for Minimum Connected Dominating Set of a Threshold Size in Ad Hoc Networks

The set of nodes constituting a minimum connected dominating set (MCDS) in a wireless ad hoc network (WANET) could be considered as the minimum number of nodes that are required to forward a broadcast message so that the message reaches all the nodes in the network. With regards to MCDS construction, we notice that smaller the transmission range for the nodes, the larger the size of the MCDS and vice-versa. Hence, from an energy efficiency point of view, it is imperative to determine the minimum transmission range (we assume uniform transmission range for all the nodes) that would be needed to construct a MCDS of a certain threshold size in WANETs. In this pursuit, we propose a binary search algorithm of logarithmic time complexity to determine the minimum uniform transmission range that would be sufficient to obtain a connected network and construct a MCDS whose size is within a threshold.