κ‐channel connectivity in cognitive radio networks for bounded tree‐width graphs

Abstract

SummaryChannel connectivity problem in cognitive radio network (CCP in CRN) is to find a channel assignment for secondary users (SUs) such that underlying graph induced by SUs (potential graph) is connected. Channel connectivity problem in CRNs has been proved to be NP‐complete for general graph and remains NP‐complete even if the underlying potential graph is the tree. Fixed parameter tractability of CCP in CRN has been of research interest because of its practicability. In this work, we have proposed novel problem of fixed parameter tractability for κ‐CCP of CRN (κ‐CCP in CRN), ie, whether a given CRN remains connected when any of κ−1 channels are reclaimed by primary users, called κ‐CCP. This is very crucial to check and design an effective channel assignment algorithm that provides connectivity to SUs on channels reclamation by primary users. To our knowledge, fixed parameter tractability of κ‐CCP in CRNs has not been studied and becoming useful because of development of 5G if the underlying potential graph has bounded tree‐width and number of channels is parameterized. We address κ‐CCP in CRN and propose an O(α)O(α)nO(1) time algorithm if the underlying potential graph is bounded by tree‐width and generates a feasible channel assignment under which given CRN is κ‐channel connected, where α is the number of channels and n is the number of SUs in CRN. We show that the κ‐CCP is fixed parameter tractable, when underlying potential graph has bounded tree‐width and number of channels is parameterized. To count the different possible potential solution of κ‐CCP, we propose a polynomial time algorithm for the corresponding enumeration problem (the number of different feasible channel assignments) Enum‐κ‐CCP on the potential graph with bounded tree‐width when the number of channels is bounded by a constant. Through simulation, we have observed that the feasibility of κ‐CCP highly depends on the available channels at each SU and number of radio present at each SU.