On the Complexity of Connectivity in Cognitive Radio Networks Through Spectrum Assignment

TL;DR

This paper explores the computational complexity of ensuring connectivity in cognitive radio networks through spectrum assignment, revealing NP-completeness in various scenarios and providing exact algorithms for connectivity determination.

Contribution

It is the first systematic study analyzing the algorithmic complexity of connectivity problems in CRNs with spectrum assignments, including NP-completeness proofs and fixed-parameter tractability results.

Findings

Connectivity determination is NP-complete in general CRNs.

Special cases with fixed channels and uniform antennae are also NP-complete.

Exact algorithms for connectivity testing are developed.

Abstract

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 NP-complete 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.