Connectivity in CRNs with bounded tree-width potential graph and its fixed parameter tractability

Abstract

Cognitive Radio Networks (CRNs) are considered as a promising solution to the spectrum shortage problem in wireless communication. We model the network of secondary users (SUs) as an undirected potential graph PG = (V (PG),E(PG)), where v ∈ V (PG) correspond to a secondary user and each edge (u, v) ∈ E(PG) represents link between nodes u and v (nodes are in within the transmission range). Two nodes having an edge between them are connected if their spectrum assignments have a common channel. In general, it is NP-complete to determine whether the network is connectable through spectrum assignment in CRN. In this paper, we propose a dynamic programming algorithm to check κ-channel connectivity of CRNs through spectrum assignment for the special case in which PG is a bounded tree-width graph. We also show that the κ-channel connectivity problems are fixed-parameter tractable. We have studied our proposed algorithm theoretically as well practically. The complexity of proposed algorithm is O(k)O(k)nO(1), where is k is the number of channels and n is number of SUs in CRN. Through simulation results, we have analysed that the channel connectivity depends on the available channels, spectrum map of each SU, antenna budget, tree-width of networks.