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A New Constant Factor Approximation for Computing 3Connected mDominating Sets in Homogeneous Wireless Networks
"... Abstract—In this paper, we study the problem of constructing quality faulttolerant Connected Dominating Sets (CDSs) in homogeneous wireless networks, which can be defined as minimum kConnected mDominating Set ((k, m)CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximat ..."
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Abstract—In this paper, we study the problem of constructing quality faulttolerant Connected Dominating Sets (CDSs) in homogeneous wireless networks, which can be defined as minimum kConnected mDominating Set ((k, m)CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximation algorithm for this problem is incomplete for k ≥ 3 in a sense that it does not generate a feasible solution in some UDGs. Based on these observations, we propose a new polynomial time approximation algorithm for computing (3,m)CDSs. We also show that our algorithm is correct and its approximation ratio is a constant. I.
Constructing Connected Dominating Sets with Bounded Diameters
 in Wireless Networks”, in Proc. International Conference on Wireless Algorithms, Systems and Applications (WASA
, 2007
"... In wireless networks, due to the lack of fixed infrastructure or centralized management, a Connected Dominating Set (CDS) of the graph representing the network is an optimum candidate to serve as the virtual backbone of a wireless network. However, constructing a minimum CDS is NPhard. Furthermore, ..."
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In wireless networks, due to the lack of fixed infrastructure or centralized management, a Connected Dominating Set (CDS) of the graph representing the network is an optimum candidate to serve as the virtual backbone of a wireless network. However, constructing a minimum CDS is NPhard. Furthermore, almost all of the existing CDS construction algorithms neglect the diameter of a CDS, which is an important factor. In this paper, we investigate the problem of constructing a CDS with a bounded diameter in wireless networks and propose a heuristic algorithm, Connected Dominating Sets with Bounded Diameters (CDSBD), with constant performance ratios for both the size and diameter of the constructed CDS. 1
Incremental Construction of kDominating Sets in Wireless Sensor Networks
, 2006
"... Given a graph G, a kdominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a kdominating set. The algorithm constructs a monotone family of dominating sets ..."
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Given a graph G, a kdominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a kdominating set. The algorithm constructs a monotone family of dominating sets D1 ⊆ D2... ⊆ Di... ⊆ Dk such that each Di is an idominating set. For unit disk graphs, the size of each of the resulting idominating sets is at most six times the optimal. 1
A Power Aware Minimum Connected Dominating Set for Wireless Sensor Networks
 Journal of Networks
, 2009
"... Abstract Connected Dominating Set (CDS) problem in unit disk graph has a significant impact on an efficient design of routing protocols in wireless sensor networks. In this paper, an algorithm is proposed for finding Minimum Connected Dominating Set (MCDS) using Dominating Set. Dominating Sets are ..."
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Abstract Connected Dominating Set (CDS) problem in unit disk graph has a significant impact on an efficient design of routing protocols in wireless sensor networks. In this paper, an algorithm is proposed for finding Minimum Connected Dominating Set (MCDS) using Dominating Set. Dominating Sets are connected by using Steiner tree. The algorithm goes through three phases. In first phase Dominating Sets are found, in second phase connectors are identified, connected through Steiner tree. In third phase the CDS obtained in second phase is pruned to obtain a MCDS. MCDS so constructed needs to adapt to the continual topology changes due to deactivation of a node due to exhaustion of battery power. These topological changes due to power constraints are taken care by a local repair algorithm that reconstructs the MCDS i.e. Power Aware MCDS, using only neighbourhood information. Simulation results indicate both the heuristics are very efficient and result in near optimal MCDS. Index Terms Connected Dominating Set, topology, virtual backbone, wireless sensor networks. away from an element of the subset forms a dominating set S. A connected dominating set (CDS) C of G is a dominating set S in which all the elements are connected i.e. it induces a connected graph. The nodes in C are called dominators and the other nodes which are one hop away from C are dominatees. To minimize the number of hops, the minimum CDS is chosen as the backbone.. The backbone is the smallest CDS and every node is adjacent to this virtual backbone. Once data is received by a dominator, it is relayed through the MCDS towards the sink for minimum hop communication. Since the nodes have equal transmission range, the CDS has to be determined for Unit Disk Graph (UDG). The figures of CDS backbone and its UDG can be shown in Figure 1a and in figure 1b respectively. The problem is known to be NPhard and requires heuristics for the determination of the CDS [2].
Maintaining CDS in Mobile Ad Hoc Networks
 in Proceedings of International Conference on Wireless Algorithms, Systems and Applications (WASA
, 2008
"... Abstract. The connected dominating set (CDS) has been generally used for routing and broadcasting in mobile ad hoc networks (MANETs). To reduce the cost of routing table maintenance, it is preferred that the size of CDS to be as small as possible. A number of protocols have been proposed to construc ..."
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Abstract. The connected dominating set (CDS) has been generally used for routing and broadcasting in mobile ad hoc networks (MANETs). To reduce the cost of routing table maintenance, it is preferred that the size of CDS to be as small as possible. A number of protocols have been proposed to construct CDS with competitive size, however only few are capable of maintaining CDS under topology changes. In this research, we propose a novel extended mobility handling algorithm which will not only shorten the recovery time of CDS mobility handling but also keep a competitive size of CDS. Our simulation results validate that the algorithm successfully achieves its design goals. In addition, we will introduce an analytical model for the convergence time and the number of messages required by the CDS construction. 1
A Dominating and Absorbent Set in Wireless Adhoc Networks with Different Transmission
 Range,” Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2007
"... Unlike a cellular or wired network, there is no base station or network infrastructure in a wireless adhoc network, in which nodes communicate with each other via peer communications. In order to make routing and flooding efficient in such an infrastructureless network, Connected Dominating Set (CD ..."
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Unlike a cellular or wired network, there is no base station or network infrastructure in a wireless adhoc network, in which nodes communicate with each other via peer communications. In order to make routing and flooding efficient in such an infrastructureless network, Connected Dominating Set (CDS) as a virtual backbone has been extensively studied. Most of the existing studies on the CDS problem have focused on unit disk graphs, where every node in a network has the same transmission range. However, nodes may have different powers due to difference in functionalities, power control, topology control, and so on. In this case, it is desirable to model such a network as a disk graph where each node has different transmission range. In this paper, we define Minimum Strongly Connected Dominating and Absorbent Set (MSCDAS) in a disk graph, which is the counterpart of minimum CDS in unit disk graph. We propose a constant approximation algorithm when the ratio of the maximum to the minimum in transmission range is bounded. We also present two heuristics and compare the performances of the proposed schemes through simulation.
A Genetic Algorithm for Constructing a Reliable MCDS
 in Probabilistic Wireless Networks, WASA, 2011.672
"... Abstract. Minimum Connected Dominating Sets (MCDSs) are used as virtual backbones for efficient routing and broadcasting in wireless networks extensively. However, the MCDS problem is NPComplete even in Unit Disk Graphs. Therefore, many heuristicbased approximation algorithms have been proposed ..."
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Abstract. Minimum Connected Dominating Sets (MCDSs) are used as virtual backbones for efficient routing and broadcasting in wireless networks extensively. However, the MCDS problem is NPComplete even in Unit Disk Graphs. Therefore, many heuristicbased approximation algorithms have been proposed recently. In these approaches, networks are deterministic where two nodes are assumed either connected or disconnected. In most real applications, however, there are many intermittently connected wireless links called lossy links, which only provide probabilistic connectivity. For wireless networks with lossy links, we propose a Probabilistic Network Model (PNM). Under this model, we measure the quality of Connected Dominating Sets (CDSs) using CDS reliability defined as the minimum upper limit of the nodetonode delivery ratio between any pair of dominators in a CDS. We attempt to construct a MCDS while its reliability is above a preset applicationspecified threshold, called Reliable MCDS (RMCDS). We claim that constructing a RMCDS is NPHard under the PNM model. We propose a novel Genetic Algorithm (GA) called RMCDSGA to solve the RMCDS problem. To evaluate the performance of RMCDSGA, we conduct comprehensive simulations. The simulation results show that compared with the traditional MCDS algorithms, RMCDSGA can construct a more reliable CDS without increasing the size of a CDS. 1
Distributed Connected Dominating Set Construction in Geometric kDisk Graphs
 University of Minnesota. He
, 2008
"... In this paper, we study the problem of minimum connected dominating set in geometric kdisk graphs. This research is motivated by the problem of virtual backbone construction in wireless ad hoc and sensor networks, where the coverage area of nodes are disks with different radii. We derive the size ..."
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In this paper, we study the problem of minimum connected dominating set in geometric kdisk graphs. This research is motivated by the problem of virtual backbone construction in wireless ad hoc and sensor networks, where the coverage area of nodes are disks with different radii. We derive the size relationship of any maximal independent set and the minimum connected dominating set in geometric kdisk graphs, and apply it to analyze the performances of two distributed connected dominating set algorithms we propose in this paper. These algorithms have a bounded performance ratio and low communication overhead, and therefore have the potential to be applied in real ad hoc and sensor networks. 1
Connected Dominating Sets
"... Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent chara ..."
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Wireless sensor networks (WSNs), consist of small nodes with sensing, computation, and wireless communications capabilities, are now widely used in many applications, including environment and habitat monitoring, traffic control, and etc. Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other wireless networks like mobile ad hoc networks or cellular networks. Hierarchical or clusterbased methods, originally proposed in wireline networks, are wellknown techniques with special advantages related to scalability and efficient communication. As such, the concept of hierarchical routing is also utilized to perform energyefficient routing in WSNs. Using a virtual backbone infrastructure which is one kind of hierarchical methods has received more attention. Thus, a Connected Dominating Set (CDS) has been recommended to serve as a virtual backbone for a WSN to reduce routing overhead. Having such a CDS simplifies routing by restricting the main routing tasks to the dominators only. Fault tolerance and routing flexibility are necessary for routing since nodes in WSNs are prone to failures and nodes may have mobility and turn on and off frequently. Thus, it is important to maintain a certain degree of redundancy in a CDS. Unfortunately, a CDS only preserves 1connectivity and it is therefore very vulnerable. Therefore, the concept of kconnected mdominating sets (kmCDS) are used to provide these redundancy. In this chapter, we first survey some existing clusterbased algorithms. After that, we focus on connected dominating set algorithms, including both centralized and distributed, for how to construct CDS. Theoretical analysis are also presented. Furthermore, some algorithms for kmCDS are described in detail.
Tighter Approximation Bounds for Minimum CDS in Unit Disk Graphs
"... Abstract Connected dominating set (CDS) in unit disk graphs has a wide range of applications in wireless ad hoc networks. A number of approximation algorithms for constructing a small CDS in unit disk graphs have been proposed in the literature. The majority of these algorithms follow a general two ..."
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Abstract Connected dominating set (CDS) in unit disk graphs has a wide range of applications in wireless ad hoc networks. A number of approximation algorithms for constructing a small CDS in unit disk graphs have been proposed in the literature. The majority of these algorithms follow a general twophased approach. The first phase constructs a dominating set, and the second phase selects additional nodes to interconnect the nodes in the dominating set. In the performance analyses of these twophased algorithms, the relation between the independence number α and the connected domination number γc of a unitdisk graph plays the key role. The bestknown relation between them is α ≤ 3 2 3 γc + 1. In this paper, we prove that α ≤ 3.4306γc + 4.8185. This relation leads to tighter upper bounds on the approximation ratios of two approximation algorithms proposed in the literature.