The first constant factor approximation for minimum partial connected dominating set problem in growth-bounded graphs

The idea of virtual backbone has emerged to improve the efficiency of flooding based routing algorithms for wireless networks. The effectiveness of virtual backbone can be improved as its size decreases. The minimum connected dominating set (CDS) problem was used to compute minimum size virtual backbone. However, as this formulation requires the virtual backbone nodes to connect all other nodes, even the size of minimum virtual backbone can be large. This observation leads to consider the minimum partial CDS problem, whose goal is to compute a CDS serving only more than a certain portion of the nodes in a given network. So far, the performance ratio of the best approximation algorithm for the problem is \(O(\ln \varDelta ),\) where \(\varDelta\) is the maximum degree of the input general graph. In this paper, we first assume the input graph is a growth-bounded graph and introduce the first constant factor approximation for the problem. Later, we show that our algorithm is an approximation for the problem in unit disk graph with a much smaller performance ratio, which is of practical interest since unit disk graph is popular to abstract homogeneous wireless networks. Finally, we conduct simulations to evaluate the average performance of our algorithm.