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In a cognitive radio network (CRN), connectivity is essential for the information exchange between secondary users (SUs). However, the unpredictable activities of primary users (PUs) may result in an unconnected network. Most of the existing works could only guarantee the CRN's connectivity with one channel reclaimed by PU, without considering a more general case that PUs request multiple channels simultaneously, and thus, a network partition may occur more likely. In this paper, first, k-channelconnectivity is defined to derive a CRN that remains connected whenever any k - 1 channels are occupied concurrently. Then, we propose both centralized and distributed topology control algorithms to ensure both the k-channel-connected and conflict-free properties. Particularly, it is accomplished by ensuring that any k - 1 independent sets (i.e., groups of SUs transmitting on the same channel) are not any vertex-cut set of the CRN. Next, the correctness of both the algorithms is verified via theoretical analysis; meanwhile, the analysis demonstrates that the proposed algorithms can achieve the target with a reasonable computation complexity, and in particular, the distributed one can work with limited local information. Finally, simulation results reveal that the proposed algorithms enable the reduction of not only the required channels but also the power consumption of the CRN.

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Fault-Tolerant Topology Control Towards <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>-Channel-Connectivity in Cognitive Radio Networks

Fault-Tolerant Topology Control Towards ${K}$ -Channel-Connectivity in Cognitive Radio Networks