Complexity of Connectivity in Cognitive Radio Networks through Spectrum Assignment

Cognitive Radio Networks (CRNs) are considered as a promising solution to the spectrum shortage problem in wireless communication. In this paper, we initiate the first systematic study on the algorithmic complexity of the connectivity problem in CRNs through spectrum assignments. We model the network of secondary users (SUs) as a potential graph, where two nodes having an edge between them are connected as long as they choose a common available channel. In the general case, where the potential graph is arbitrary and the SUs may have different number of antennae, we prove that it is NPcomplete to determine whether the network is connectable even if there are only two channels. For the special case where 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 the special cases in which the potential graph is complete, a tree, or a graph with bounded treewidth, we prove the problem is NP-complete and fixed-parameter tractable (FPT) when parameterized by the number of channels. Exact algorithms are also derived to determine the connectability of a given cognitive radio network. A preliminary version of this paper appears in ALGOSENSORS 2012 [13]. The main extensions are that we give more details of our results and investigate the special case where the potential graphs are of bounded treewidth. Hongyu Liang, Haisheng Tan(Corresponding Author), Yuexuan Wang Institute for Theoretical Computer Science, IIIS, Tsinghua University, Beijing, China E-mail: [email protected], {tan,wangyuexuan}@mail.tsinghua.edu.cn Tiancheng Lou Google Inc., California, USA E-mail: [email protected] Dongxiao Yu Department of Computer Science, the University of Hong Kong, Hong Kong, China 2 Hongyu Liang et al.