Connected dominating set (CDS) is a representative technique for constructing virtual backbones of wireless networks to improve the efficiency of communication. Most of existing works on CDS aim to construct the minimum CDS (MCDS). However, MCDS may not be sufficient in cognitive radio networks where communication links are prone to failure due to random activities of primary users. To solve the problem, an algorithm is proposed in this paper to construct a CDS with redundancy and the maximum spectrums in CRNs. Moreover, with an integer programming formulation, an algorithm is designed to obtain the minimum 2-conneted 2-dominating set with maximum spectrums (MSs) in CRNs. To the best of our knowledge, this is the first integer programming formulation for the problem and the concept of MSs is put forward first. Simulation results indicate that our algorithm performs well.
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