Complexity of Connectivity in Cognitive Radio Networks through Spectrum Assignment

Abstract

Cognitive Radio Networks (CRNs) are considered as a promising solution to the spectrum shortage problem in wireless communication. In this paper, we address the algorithmic complexity of the connectivity problem in CRNs through spectrum assignment. We model the network of secondary users (SUs) as a potential graph, where if two nodes have an edge between them, they are connected as long as they choose a common available channel. In the general case, where the potential graph is arbitrary and SUs may have different number of antennae, we prove that it is NP-complete to determine whether the network is connectable even if there are only two channels. For the special case when the number of channels is constant and all the SUs have the same number of antennae, which is more than one but less than the number of channels, the problem is also NP-complete. For special cases that the potential graph is complete or a tree, we prove the problem is NP-complete and fixed-parameter tractable (FPT) when parameterized by the number of channels. Furthermore, exact algorithms are derived to determine the connectivity.