A degree-based heuristic for strongly connected dominating-absorbent sets in wireless ad-hoc networks

Virtual backbones of asymmetric wireless networks are special sub-nets through which routing can be performed. Such backbone must be as small as possible, and must be able to receive and transmit messages from/to each and every node in the network. The corresponding graph theoretic problem takes a directed graph as input and seeks a strongly connected dominating-absorbent set of smallest possible cardinality. We introduce a hybrid heuristic for this problem, in which we combine low-degree vertex elimination and high-degree vertex selection. This simple and efficient method yields very promising experimental results, outperforming known heuristic algorithms.