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An extended localized algorithm for connected dominating set formation in ad hoc wireless networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2004
"... Efficient routing among a set of mobile hosts is one of the most important functions in ad hoc wireless networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts in the sy ..."
Abstract

Cited by 143 (15 self)
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Efficient routing among a set of mobile hosts is one of the most important functions in ad hoc wireless networks. Routing based on a connected dominating set is a promising approach, where the search space for a route is reduced to the hosts in the set. A set is dominating if all the hosts in the system are either in the set or neighbors of hosts in the set. The efficiency of dominatingsetbased routing mainly depends on the overhead introduced in the formation of the dominating set and the size of the dominating set. In this paper, we first review a localized formation of a connected dominating set called marking process and dominatingsetbased routing. Then, we propose a dominant pruning rule to reduce the size of the dominating set. This dominant pruning rule (called Rule k) is a generalization of two existing rules (called Rule 1 and Rule 2, respectively). We prove that the vertex set derived by applying Rule k is still a connected dominating set. Rule k is more effective in reducing the dominating set derived from the marking process than the combination of Rules 1 and 2 and, surprisingly, in a restricted implementation with local neighborhood information, Rule k has the same communication complexity and less computation complexity. Simulation results confirm that Rule k outperforms Rules 1 and 2, especially in networks with relatively high vertex degree and high percentage of unidirectional links. We also prove that an upper bound exists on the average size of the dominating set derived from Rule k in its restricted implementation.
Messageoptimal connected dominating sets in mobile ad hoc networks
 in Proceedings of The Third ACM International Symposium on Mobile Ad Hoc Networking & Computing (MobiHoc), 2002
"... A connected dominating set (CDS) for a graph G(V,E) isa subset V ′ of V, such that each node in V − V ′ is adjacent to some node in V ′,andV ′ induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NPhard to find a minimum ..."
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Cited by 110 (6 self)
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A connected dominating set (CDS) for a graph G(V,E) isa subset V ′ of V, such that each node in V − V ′ is adjacent to some node in V ′,andV ′ induces a connected subgraph. A CDS has been proposed as a virtual backbone for routing in wireless ad hoc networks. However, it is NPhard to find a minimum connected dominating set (MCDS). Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a very poor approximation ratio, and from high time complexity and message complexity. Recently, new distributed heuristics for constructing a CDS were developed, with constant approximation ratio of 8. These new heuristics are based on a construction of a spanning tree, which makes it very costly in terms of communication overhead to maintain the CDS in the case of mobility and topology changes. In this paper, we propose the first distributed approximation algorithm to construct a MCDS for the unitdiskgraph with a constant approximation ratio, and linear time and linear message complexity. This algorithm is fully localized, and does not depend on the spanning tree. Thus, the maintenance of the CDS after changes of topology guarantees the maintenance of the same approximation ratio. In this algorithm each node requires knowledge of its singlehop neighbors, and only a constant number of twohop and threehop neighbors. The message length is O(log n) bits. Keywords ad hoc networks, connected dominating set, maximal independent
A Generic Distributed Broadcast Scheme in Ad Hoc Wireless Networks,”
 IEEE Transactions on Computer,
, 2004
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Clustering Algorithms for Ad Hoc Wireless Networks
, 2004
"... An ad hoc network is a multihop wireless communication network supporting mobile users without any existing infrastructure. To become commercially successful, the technology must allow networks to support many users. A complication is that addressing and routing in ad hoc networks does not scale u ..."
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Cited by 51 (2 self)
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An ad hoc network is a multihop wireless communication network supporting mobile users without any existing infrastructure. To become commercially successful, the technology must allow networks to support many users. A complication is that addressing and routing in ad hoc networks does not scale up as easily as in the Internet. By introducing hierarchical addresses to ad hoc networks, we can effectively address this complication. Clustering provides a method to build and maintain hierarchical addresses in ad hoc networks. Here, we survey several clustering algorithms, concentrating on those that are based on graph domination. In addition, we describe results that show that building clustered hierarchies is affordable and that clustering algorithms can also be used to build virtual backbones to enhance network quality of service.
A Zonal Algorithm for Clustering Ad Hoc Networks
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, IJFCS
, 2003
"... A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multihop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which ..."
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Cited by 40 (1 self)
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A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multihop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which is more suitable for clustering MANETs is the weaklyconnected dominating set. A cluster is defined to be the set of vertices dominated by a particular vertex in the dominating set. As it is NPcomplete to determine whether a given graph has a weaklyconnected dominating set of a particular size, we present a zonal distributed algorithm for finding small weaklyconnected dominating sets. In this new approach, we divide the graph into regions, construct a weaklyconnected dominating set for each region, and make adjustments along the borders of the regions to produce a weaklyconnected dominating set of the entire graph. We present
A Distributed Coverage and ConnectivityCentric Technique for Selecting Active Nodes in Wireless Sensor Networks.
 IEEE Transactions on Computers
, 2005
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Connected dominating sets in wireless networks with different transmission ranges
 IEEE TRANSACTIONS ON MOBILE COMPUTING
, 2007
"... 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 wireles ..."
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Cited by 32 (4 self)
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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.
On greedy construction of connected dominating sets in wireless networks
 NSF International Workshop on Theoretical Aspects of Wireless Ad Hoc, Sensor and PeertoPeer Networks
, 2004
"... Due to the fact that there is no fixed infrastructure or centralized management in ad hoc wireless networks, a Connected Dominating Set (CDS) of the graph representing the network is widely used as the virtual backbone of the network. Constructing a minimum CDS is NPhard. In this paper, we propose ..."
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Cited by 29 (8 self)
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Due to the fact that there is no fixed infrastructure or centralized management in ad hoc wireless networks, a Connected Dominating Set (CDS) of the graph representing the network is widely used as the virtual backbone of the network. Constructing a minimum CDS is NPhard. In this paper, we propose a completely localized distributed algorithm which is rCDS to construct a CDS with constant performance ratio. Our algorithm is better at maintenance since there is no need to build a tree or select a leader which are the common methods used in most of the distributed but serialized algorithms. We also compare our algorithm with other localized algorithms. The theoretical and simulation results show that our algorithm has a better performance ratio and constructs a CDS with smaller size in most cases. 1
Extended Dominating Set and Its Applications in Ad Hoc Networks Using Cooperative Communication
 IEEE TRANS. PARALLEL AND DISTRIBUTED SYSTEMS, ACCEPTED FOR PUBLICATION
, 2005
"... We propose a notion of extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates d ..."
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Cited by 24 (5 self)
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We propose a notion of extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates diversity and combats the effects of fading. We first show the NPcompleteness of the minimum extended dominating set problem. Then, several heuristic algorithms, global and local, for constructing a small extended dominating set are proposed. These are nontrivial extensions of the existing algorithms for the regular dominating set problem. The application of the extended dominating set in efficient broadcasting is also discussed. The performance analysis includes an analytical study in terms of approximation ratio and a simulation study of the average size of the extended dominating set derived from the proposed algorithms.
A New Heuristic For The Minimum Connected Dominating Set Problem On Ad Hoc Wireless Networks
, 2003
"... Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is adjacent to at least one vertex in D. Efficient algorithms for computing the minimum connected dominating set (MCDS) are essential for solving many practical problems, such as finding a minimum size backbo ..."
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Cited by 24 (3 self)
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Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is adjacent to at least one vertex in D. Efficient algorithms for computing the minimum connected dominating set (MCDS) are essential for solving many practical problems, such as finding a minimum size backbone in ad hoc networks. Wireless ad hoc networks appear in a wide variety of applications, including mobile commerce, search and discovery, and military battlefield. In this chapter we propose a new efficient heuristic algorithm for the minimum connected dominating set problem. The algorithm starts with a feasible solution containing all vertices of the graph. Then it reduces the size of the CDS by excluding some vertices using a greedy criterion. We also discuss a distributed version of this algorithm. The results of numerical testing show that, despite its simplicity, the proposed algorithm is competitive with other existing approaches. 1.