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87
Minimum energy mobile wireless networks revisited
 In IEEE International Conference on Communications (ICC
, 2001
"... Energy conservation is a critical issue in designing wireless ad hoc networks, as the nodes are powered by batteries only. Given a set of wireless network nodes, the directed weighted transmission graph Gt has an edge uv if and only if node v is in the transmission range of node u and the weight of ..."
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Cited by 173 (9 self)
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Energy conservation is a critical issue in designing wireless ad hoc networks, as the nodes are powered by batteries only. Given a set of wireless network nodes, the directed weighted transmission graph Gt has an edge uv if and only if node v is in the transmission range of node u and the weight of uv is typically defined as II,,vll + c for a constant 2 <_ t ~ < 5 and c> O. The minimum power topology Gm is the smallest subgraph of Gt that contains the shortest paths between all pairs of nodes, i.e., the union of all shortest paths. In this paper, we described a distributed positionbased networking protocol to construct an enclosure graph G~, which is an approximation of Gin. The time complexity of each node u is O(min(dG ~ (u)dG ~ (u), dG ~ (u) log dG ~ (u))), where dc(u) is the degree of node u in a graph G. The space required at each node to compute the minimum power topology is O(dG ~ (u)). This improves the previous result that computes Gm in O(dG, (u) a) time using O(dGt(U) 2) spaces. We also show that the average degree dG,(u) is usually a constant, which is at most 6. Our result is first developed for stationary network and then extended to mobile networks. I.
Coverage in Wireless Adhoc Sensor Networks
, 2002
"... Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this pape ..."
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Cited by 166 (11 self)
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Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the bestcoverage problem raised in [1]. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum bestcoverage path with the least energy consumption. We also consider how to find an optimum bestcoveragepath that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.
Distributed Construction of a Planar Spanner and Routing for Ad Hoc Wireless Networks
, 2002
"... Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more acc ..."
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Cited by 140 (26 self)
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Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unitdisk graph UDG , in which a link in between two nodes exist only if the distance in between them is at most the maximum transmission range.
Geometric Spanners for Wireless Ad Hoc Networks
 IEEE Transactions on Parallel and Distributed Systems
, 2003
"... We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network. ..."
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Cited by 96 (27 self)
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We propose a new geometric spanner for static wireless ad hoc networks, which can be constructed efficiently in a localized manner. It integrates the connected dominating set and the local Delaunay graph to form a backbone of the wireless network.
Localized Delaunay Triangulation with Application in Ad Hoc Wireless Networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2003
"... Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two grap ..."
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Cited by 94 (21 self)
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Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. [11] recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unitdisk graph (UDG), in which a link uv exists only if the distance kuvk is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2.5spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unitdisk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is Oðn log nÞ bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
 In DIALMPOMC
, 2003
"... We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delauna ..."
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Cited by 93 (20 self)
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We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + ⌈ 2π α ⌉; (3) it is a tspanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max { π α,πsin 2 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is its 2hop neighbors in the original unit disk graph. Here Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4 √ 3 9 π. And the adjustable parameter α satisfies 0 <α<π/3. In addition, experiments are conducted to show this topology is efficient in practice, compared with other wellknown topologies used in wireless ad hoc networks. Previously, only centralized method [5] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of their centralized method takes O(n 2) communications in the worst case. No localized methods were known previously for constructing bounded degree planar spanner.
Fault Tolerant Deployment and Topology Control in Wireless Networks
 In Proceedings of the Fourth ACM Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc
, 2003
"... This paper investigate fault tolerance for wireless ad hoc networks. We consider a largescale of wireless networks whose nodes are distributed randomly in a unitarea square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ..."
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Cited by 73 (3 self)
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This paper investigate fault tolerance for wireless ad hoc networks. We consider a largescale of wireless networks whose nodes are distributed randomly in a unitarea square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ) in which two nodes are connected if their Euclidean distance is no more than rn .
Localized Topology Control for Heterogeneous Wireless Adhoc Networks
"... We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sp ..."
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Cited by 69 (11 self)
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We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sparse and power efficient topologies in heterogeneous network environment with low communication cost. The first structure is sparse and can be used for broadcasting. While the second structure keeps the minimum power consumption path, and the third structure is a length and power spanner with a bounded degree. Both the second and third structures are power efficient and can be used for unicast. Here a structure is power efficient if the total power consumption of the least cost path connecting any two nodes in it is no more than a small constant factor of that in the original heterogeneous communication graph. All our methods use at most O(n) total messages, where each message has O(log n) bits.
Sparse Power Efficient Topology for Wireless Networks
 Journal of Parallel and Distributed Computing
, 2002
"... dimensional plane. Each wireless node has an omnidirectional antenna. This is attractive for a single We consider how to construct power wireless ad mission of a node can be received by many nodes within hoc networks. We propose two different methods its vicinity. In the most common powerattenuat ..."
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Cited by 66 (23 self)
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dimensional plane. Each wireless node has an omnidirectional antenna. This is attractive for a single We consider how to construct power wireless ad mission of a node can be received by many nodes within hoc networks. We propose two different methods its vicinity. In the most common powerattenuation several wellknown proximity graphs including Gabriel graph and Yao which can be constructed locally and Firstly, we combine the Gabriel and model, the power needed to support a link is where is the distance between and v, is a real constant between 2 and 4 dependent on the wireless transmission environment. By a proper scaling, we sume that all nodes have the maximum transmission range equal to one unit. These wireless nodes define a unit disk graph in which there is an edge between two nodes if and only if their Euclidean distance is at most one. The size of the unit disk graph could be large as the square order of the number of network nodes. Given a unicasting or multicasting request, the routing problem is to find a route whose energy consumption is within a small constant factor of the optimum route. Notice that the time complexity of computing the shortest path connecting two nodes is the Yao structure. The constructed topology has at most edges and each node has a bounded outdegree.
Localized algorithms for energy efficient topology in wireless ad hoc networks
 In ACM MobiHoc’04
, 2004
"... Abstract. Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireles ..."
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Cited by 66 (8 self)
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Abstract. Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireless ad hoc networks. Our first method constructs a structure with the following attractive properties: power efficient, bounded node degree, and planar. Its power stretch factor is at most ρ = 1 1−(2 sin π k)β, and each node only has to maintain at most k + 5 neighbors where the integer k> 6 is an adjustable parameter, and β is a real constant between 2 and 5 depending on the wireless transmission environment. It can be constructed and maintained locally and dynamically. Moreover, by assuming that the node ID and its position can be represented in O(log n) bits each for a wireless network of n nodes, we show that the structure can be constructed using at most 24n messages, where each message is O(log n) bits. Our second method improves the degree bound to k, relaxes the theoretical power spanning ratio to ρ = √ 2 β 1−(2 √ 2 sin π, where k> 8 is an adjustable parameter, and keeps all other)β k properties. We show that the second structure can be constructed using at most 3n messages, where each message has size of O(log n) bits. We also experimentally evaluate the performance of these new energy efficient network topologies. The theoretical results are corroborated by the simulations: these structures are more efficient in practice, compared with other known structures used in wireless ad hoc networks and are easier to construct. In addition, the power assignment based on our new structures shows low energy cost and small interference at each wireless node.