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On Constructing kConnected kDominating Set in Wireless Networks
 In Proceedings of the 19 th International Parallel & Distributed Processing Symposium (IPDPS
, 2005
"... An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. In this paper, we propose ..."
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Cited by 28 (1 self)
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An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small virtual backbone for high efficiency. In this paper, we propose the construction of a kconnected kdominating set (kCDS) as a backbone to balance efficiency and fault tolerance. Four localized kCDS construction protocols are proposed. The first protocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on the value of k and network condition, such as network size and node density. The second one maintains a fixed backbone node degree of Bk, where Bk also depends on the network condition. The third protocol is a deterministic approach. It extends Wu and Dai’s coverage condition, which is originally designed for 1CDS construction, to ensure the formation of a kCDS. The last protocol is a hybrid of probabilistic and deterministic approaches. It provides a generic framework that can convert many existing CDS algorithms into kCDS algorithms. These protocols are evaluated via a simulation study. Key words: Connected dominating set (CDS), kvertex connectivity, localized algorithms, simulation, wireless ad hoc and sensor networks. PACS: Preprint submitted to Elsevier Science 23 September 2005
Extended multipoint relays to determine connected dominating sets in MANETs
 IEEE Transactions on Computers
, 2006
"... Abstract — Multipoint relays (MPR) [1] provides a localized and optimized way of broadcasting messages in a mobile ad hoc network (MANET). Using 2hop neighborhood information, each node determines a small set of forward neighbors to relay messages. Selected forward nodes form a connected dominating ..."
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Cited by 24 (0 self)
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Abstract — Multipoint relays (MPR) [1] provides a localized and optimized way of broadcasting messages in a mobile ad hoc network (MANET). Using 2hop neighborhood information, each node determines a small set of forward neighbors to relay messages. Selected forward nodes form a connected dominating set (CDS) to ensure full coverage. Adjih, Jacquet, and Viennot [2] proposed a novel localized algorithm to construct a small CDS based on the original MPR. In this paper, we provide several extensions to generate a smaller CDS using 3hop neighborhood information to cover each node’s 2hop neighbor set. In addition, we extend the notion of coverage in the original MPR. We show that the extended MPR has a constant local approximation ratio compared with a logarithmic local ratio in the original MPR. The effectiveness of our approach is confirmed through a simulation study.
On connected multiple point coverage in wireless sensor networks
 Journal of Wireless Information Networks
, 2006
"... Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing ..."
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Cited by 24 (0 self)
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Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing point coverage. In this case, all the points of wireless devices could be used to represent the whole area, and the working sensors are supposed to cover all the sensors. Many applications related to security and reliability require guaranteed kcoverage of the area at all times. In this paper, we formalize the k(Connected) Coverage Set (kCCS/kCS) problems, develop a linear programming algorithm, and design two nonglobal solutions for them. Some theoretical analysis is also provided followed by simulation results. Index Terms — Coverage problem, linear programming, localized algorithms, reliability, wireless sensor networks.
Efficient Broadcasting with Guaranteed Coverage in Mobile Ad Hoc Networks
 IEEE TRANSACTIONS ON MOBILE COMPUTING
, 2005
"... We study an efficient broadcast scheme in mobile ad hoc networks (MANETs). The objective is to determine a small set of forward nodes to ensure full coverage. We first study several methods that guarantee coverage when the local view of each node on its neighborhood information is updated in a time ..."
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Cited by 23 (2 self)
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We study an efficient broadcast scheme in mobile ad hoc networks (MANETs). The objective is to determine a small set of forward nodes to ensure full coverage. We first study several methods that guarantee coverage when the local view of each node on its neighborhood information is updated in a timely manner. Then we consider a general case where nodes move even during the broadcast process, making it impractical to maintain uptodate and consistent local views. A formal framework is used to model inaccurate local views in MANETs, where full coverage is guaranteed if three sufficient conditions, connectivity, link availability, and consistency, are met. Three solutions are proposed to satisfy those conditions. First, we give a minimal transmission range that maintains the connectivity of the virtual network constructed from local views. Then, we use two transmission ranges, one for neighborhood information collection and the other for actual data transmission, to form a buffer zone that guarantees the availability of logical links in the physical network. Finally, we propose a mechanism called aggregated local view to ensure consistent local views. By these, we extend Wu and Dai’s coverage condition for broadcasting in a network with mobile nodes. The effectiveness of the proposed scheme is confirmed via both performance analysis and simulation study.
Clustering wireless ad hoc networks with weakly connected dominating set
, 2007
"... The increasing popular personal communications and mobile computing require a wireless network infrastructure that supports selfconfiguration and selfmanagement. Efficient clustering protocol for constructing virtual backbone is becoming one of the most important issues in wireless ad hoc networks. ..."
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Cited by 18 (0 self)
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The increasing popular personal communications and mobile computing require a wireless network infrastructure that supports selfconfiguration and selfmanagement. Efficient clustering protocol for constructing virtual backbone is becoming one of the most important issues in wireless ad hoc networks. The weakly connected dominating set (WCDS) is very suitable for cluster formation. As finding the minimum WCDS in an arbitrary graph is a NPHard problem, we propose an areabased distributed algorithm for WCDS construction in wireless ad hoc networks with time and message complexity O(n). This Area algorithm is divided into three phases: area partition, WCDS construction for each area and adjustment along the area borders. We confirm the effectiveness of our algorithm through analysis and comprehensive simulation study. The number of nodes in the WCDS constructed by this Area algorithm is up to around 50 % less than that constructed by the previous wellknown algorithm.
Construction Algorithms for kConnected mDominating Sets in Wireless Sensor Networks
 MOBIHOC'08
, 2008
"... A Connected Dominating Set (CDS) working as a virtual backbone is an effective way to decrease the overhead of routing in a wireless sensor network. Furthermore, a kConnected mDominating Set (kmCDS) is necessary for fault tolerance and routing flexibility. Some approximation algorithms have been p ..."
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Cited by 14 (2 self)
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A Connected Dominating Set (CDS) working as a virtual backbone is an effective way to decrease the overhead of routing in a wireless sensor network. Furthermore, a kConnected mDominating Set (kmCDS) is necessary for fault tolerance and routing flexibility. Some approximation algorithms have been proposed to construct a kmCDS. However, most of them only consider some special cases where k = 1, 2 or k ≤ m, or are not easy to implement, or have high message complexity. In this paper, we propose a novel distributed algorithm LDA with low message complexity to construct a kmCDS for general k and m whose size is guaranteed to be within a small constant factor of the optimal solution when the maximum node degree is a constant. We also propose one centralized algorithm ICGA with a constant performance ratio to construct a kmCDS. Theoretical analysis as well as simulation results are shown to evaluate the proposed algorithms.
Connected dominating sets in wireless networks with different transmission ranges
 IEEE transactions on mobile computing
, 2007
"... Abstract—Since there is no fixed infrastructure or centralized management in wireless ad hoc networks, a Connected Dominating Set (CDS) has been proposed to serve as a virtual backbone. The CDS of a graph representing a network has a significant impact on the efficient design of routing protocols in ..."
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Cited by 14 (3 self)
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Abstract—Since there is no fixed infrastructure or centralized management in wireless ad hoc networks, a Connected Dominating Set (CDS) has been proposed to serve as a virtual backbone. The CDS of a graph representing a network has a significant impact on the efficient design of routing protocols in wireless networks. This problem has been studied extensively in Unit Disk Graphs (UDG), in which all nodes have the same transmission ranges. However, in practice, the transmission ranges of all nodes are not necessarily equal. In this paper, we model a network as a disk graph and introduce the CDS problem in disk graphs. We present two efficient approximation algorithms to obtain a minimum CDS. The performance ratio of these algorithms is constant if the ratio of the maximum transmission range over the minimum transmission range in the network is bounded. These algorithms can be implemented as distributed algorithms. Furthermore, we show a size relationship between a maximal independent set and a CDS as well as a bound of the maximum number of independent neighbors of a node in disk graphs. The theoretical analysis and simulation results are also presented to verify our approaches. Index Terms—Connected dominating set, independent set, disk graph, wireless network, virtual backbone. 1
A new algorithm for finding trees with many leaves
, 2001
"... We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf OutTree and Directed Maximum Leaf Spanning OutTree in the case of directed grap ..."
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Cited by 12 (1 self)
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We present an algorithm that finds trees with at least k leaves in undirected and directed graphs. These problems are known as Maximum Leaf Spanning Tree for undirected graphs, and, respectively, Directed Maximum Leaf OutTree and Directed Maximum Leaf Spanning OutTree in the case of directed graphs. The run time of our algorithm is O(poly(V ) + 4 k k 2) on undirected graphs, and O(4 k V ·E) on directed graphs. Currently, the fastest algorithms for these problems have run times of O(poly(n) + 6.75 k poly(k)) and 2 O(k log k) poly(n), respectively.
T.: Distributed approximation of capacitated dominating sets
 In: Proc. 19th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2007
"... We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardin ..."
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Cited by 12 (1 self)
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We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently nonlocal, i.e., every distributed algorithm achieving a nontrivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter ɛ> 0, capacities can be violated by a factor of 1 + ɛ, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bicriteria algorithm that achieves an O(log ∆)approximation in time O(log 3 n + log(n)/ɛ), where n and ∆ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the nonuniform problem remains entirely nonlocal.
Efficient broadcasting in ad hoc wireless networks using directional antennas
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2006
"... Using directional antennas to conserve bandwidth and energy consumption in ad hoc wireless networks (or simply ad hoc networks) is becoming popular in recent years. However, applications of directional antennas for broadcasting have been limited. We propose a novel broadcast protocol called directio ..."
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Cited by 10 (5 self)
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Using directional antennas to conserve bandwidth and energy consumption in ad hoc wireless networks (or simply ad hoc networks) is becoming popular in recent years. However, applications of directional antennas for broadcasting have been limited. We propose a novel broadcast protocol called directional selfpruning (DSP) for ad hoc wireless networks using directional antennas. DSP is a nontrivial generalization of an existing localized deterministic broadcast protocol using omnidirectional antennas. Compared with its omnidirectional predecessor, DSP uses about the same number of forward nodes to relay the broadcast packet, while the number of forward directions that each forward node uses in transmission is significantly reduced. With the lower broadcast redundancy, DSP is more bandwidth and energyefficient. DSP is based on 2hop neighborhood information and does not rely on location or angleofarrival (AoA) information. Two special cases of DSP are discussed: the first one preserves shortest paths in reactive routing discoveries; the second one uses the directional reception mode to minimize broadcast redundancy. DSP is a localized protocol. Its expected number of forward nodes is Oð1Þ times the optimal value. An extensive simulation study using both custom and ns2 simulators shows that DSP significantly outperforms both omnidirectional broadcast protocols and existing directional broadcast protocols.