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Topology control is one vital factor to a wireless network's efficiency. A Connected Dominating Set (CDS) can be a useful basis of a backbone topology construction. In this paper, a special CDS, named α Minimum routing Cost CDS (α-MOC-CDS), will be studied to improve the performance of CDS based broadcasting and routing. In this paper, we prove that construction of a minimum α-MOC-CDS is NP-hard in a general graph and we propose a heuristic algorithm for construction of α-MOC-CDS.