Strongly connected dominating and absorbing set in directed disk graph

Abstract

A heterogeneous wireless network can be modelled as a directed disk graph, in which a sensor u can receive signals from sensor v if and only if u is within the transmission range of v. A virtual backbone of such a network is a strongly connected dominating and absorbing set (SCDAS). This paper presents a (2 + ε)-approximation algorithm for the minimum dominating and absorbing set problem (DAS), which, as far as we know, is the first one achieving a constant approximation ratio for DAS without requiring a bounded ratio of maximum transmission range over minimum transmission range. Based on such a DAS, a (4 + 3 ln(2 + ε)opt + ε)-approximation algorithm for SCDAS is presented, where opt is the size of an optimal SCDAS, which improves on the previous approximation ratio (3H(n − 1) − 1), where n is the number of nodes, and H(·) is the Harmonic function.