1 Constructing Connected-Dominating-Set with Maximum Lifetime in Cognitive Radio Networks Zhiyong Lin 1,2 , Hai Liu 2 , Xiaowen Chu 2 , Yiu-Wing Leung 2 , Ivan Stojmenovic 3,4 1 Dept of Computer Science, GuangDong Polytechnic Normal University, China 2 Dept of Computer Science, Hong Kong Baptist University 3 SITE, University of Ottawa; 4 School of Software, Tsinghua University, Beijing 100084, China Abstract—Connected-dominating-set (CDS) is a representative technique for constructing virtual backbones of wireless networks and thus facilitates implementation of many tasks including broadcasting, routing, etc. Most of existing works on CDS aim at constructing the minimum CDS (MCDS), so as to reduce the communication overhead over the CDS. However, MCDS may not work well in cognitive radio networks (CRNs) where communication links are prone to failure due to stochastic activities of primary users (PUs). A MCDS without consideration of the stochastic activities of PUs easily becomes invalid when the PUs become active. This study addresses a new CDS construction problem by considering the PUs’ activities. Our problem is to maximize the lifetime of the CDS while minimizing the size of the CDS, where the lifetime of a CDS is defined as the expected duration that the CDS is maintained valid. We show that the problem is NP-hard and propose a three-phase centralized algorithm. Given a CRN, the centralized algorithm can compute a CDS such that the lifetime of the CDS is maximized (optimal), and the size of the CDS is upper-bounded. We further present a two-phase localized algorithm which requires 2-hop information. Extensive simulations are conducted to evaluate the proposed algorithms. Index Terms—cognitive radio, connected-dominating-set, lifetime, fault tolerance. ——————————  —————————— 1 INTRODUCTION OGNITIVE Radio Network (CRN) has been pro- posed as a new kind of wireless networking paradigm, aiming at alleviating the severe scarcity in unlicensed spectrum as well as improving the efficiency of li- censed spectrum usage. A CRN is a group of unli- censed users (or cognitive users, CUs) equipped with cognitive radios who coexist with the licensed users (or primary users, PUs) in the same geographic area. With cognitive radios, CUs are able to sense the li- censed spectrum and opportunistically access the idle channels in the licensed spectrum of PUs without caus- ing interference to the PUs. CUs must vacate all the related channels once these channels are reclaimed by PUs for their transmissions. In a CRN, therefore, the set of available channels for a CU dynamically changes over time due to unpredictable activities of PUs. Such a unique characteristic distinguishes CRNs from con- ventional wireless networks where all nodes usually operate over the same and static channels. The concept of connected-dominating-set (CDS) plays a crucial role in the management and mainte- nance of wireless networks, e.g., wireless ad hoc net- works. A dominating set (DS) of a given graph G is a set of nodes such that each node of G is either in the set or is adjacent to a node of the set. A CDS is defined as a connected DS. The nodes in a CDS are referred to as dominators and the nodes other than dominators are referred to as dominatees. A CDS usually serves as vir- tual backbone in conventional wireless networks to facilitate tasks such as broadcasting, routing, and con- nectivity management [1] [2]. For instance, broadcast- ing in a wireless ad hoc network could be simplified by letting each node of a CDS transmit the broadcast message once. Such benefit brought from CDS could be extended to the broadcasting in CRNs. Currently, study of broadcasting in CRNs is still in its infant stage (see [3] and the relevant references therein). The exist- ing broadcasting protocols for CRNs are all non-CDS- based. These non-CDS-based approaches are compli- cated, and on the other hand, may not be efficient, since all CUs in the network are potentially requested to complete the broadcasting operation. CDS-based approaches provide a promising way to the broadcast- ing problem. For example, if a CDS of a CRN is availa- ble, we can restrict the broadcasting operation to only the CUs in the CDS and let each dominator transmit the broadcast message to all its 1-hop neighbors (Mul- tiple transmissions may be required at each dominator in the multi-channel environment of CRNs). With the CDS-based approaches, only a small fraction of CUs is involved in the broadcasting operation which makes the operation simpler and more efficient. However, the CDS-based broadcasting approaches raise a new issue of constructing CDS in CRNs. In this study, we take the first step toward addressing the CDS construction problem in CRNs. Extensive works have been done in constructing CDS for ad hoc networks, wireless sensor networks, and wireless mesh networks. Most of these works aim to construct the minimum CDS (MCDS), i.e., the CDS with the minimum size. Notice that the communica- tion tasks are normally undertaken by the nodes in CDS. A CDS with the minimum size reduces the over- all communication overhead and thus prolongs the C