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Connected Dominating Sets (CDSs) can serve as virtual backbones for wireless networks. A smaller virtual backbone incurs less maintenance overhead. Unfortunately, computing a minimum size CDS is NP-hard, and thus most researchers in this area concentrate on how to construct smaller CDSs. However, people neglected other important metrics of network, such as diameter and average hop distances between two communication parties. In this paper, we investigate the problem of constructing quality CDS in terms of size, diameter, and Average Backbone Path Length (ABPL). We present two centralized algorithms having constant performance ratios for its size and diameter of the constructed CDS. Especially, the size of CDS computed by the second algorithm is no more than 6.906 times of its optimal solution. Furthermore, we give its distributed version, which not only can be implemented in real situation …