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126
ConstantTime Distributed Dominating Set Approximation
 In Proc. of the 22 nd ACM Symposium on the Principles of Distributed Computing (PODC
, 2003
"... Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set ..."
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Cited by 112 (24 self)
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Finding a small dominating set is one of the most fundamental problems of traditional graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary parameter k and maximum degree #, our algorithm computes a dominating set of expected size O k# log #DSOPT rounds where each node has to send O k messages of size O(log #). This is the first algorithm which achieves a nontrivial approximation ratio in a constant number of rounds.
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 105 (10 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
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 72 (8 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.
Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and LinearSize Skeletons (Extended Abstract)
"... Motivated by routing issues in ad hoc networks, we present polylogarithmictime distributed algorithms for two problems. Given a network, we first show how to compute connected and weakly connected dominating sets whose size is at most O(log #) times optimal, # being the maximum degree of the input ..."
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Cited by 57 (3 self)
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Motivated by routing issues in ad hoc networks, we present polylogarithmictime distributed algorithms for two problems. Given a network, we first show how to compute connected and weakly connected dominating sets whose size is at most O(log #) times optimal, # being the maximum degree of the input network. This is bestpossible if NP ] and if the processors are limited to polynomialtime computation. We then show how to construct dominating sets which satisfy the above properties, as well as the "low stretch" property that any two adjacent nodes in the network have their dominators at a distance of at most O(log n) in the network. (Given a dominating set S, a dominator of a vertex u is any v S such that the distance between u and v is at most one.) We also show our time bounds to be essentially optimal.
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 53 (2 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 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 44 (2 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.
Equilibria in topology control games for ad hoc networks
 in: Proceedings in DIALMPOMC Mobicom
, 2003
"... Abstract. We study topology control problems in ad hoc networks where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maxim ..."
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Cited by 36 (3 self)
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Abstract. We study topology control problems in ad hoc networks where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that—among the games we define—these can only be guaranteed to exist if each network node is required to be connected to all other nodes (we call this the STRONG CONNECTIVITY GAME). For a variation called CONNECTIVITY GAME, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that Nash equilibria do not necessarily exist. We further study how to find Nash equilibria with incentivecompatible algorithms and compare the cost of Nash equilibria to the cost of a social optimum, which is a radius assignment that minimizes the total cost in a network where nodes cooperate. We also study variations of the games; one where nodes not only have to be connected, but kconnected, and one that we call the REACHABILITY GAME, where nodes have to reach as many other nodes as possible, while keeping costs low. We extend our study of the STRONG CONNECTIVITY GAME and the CONNECTIVITY GAME to wireless networks with directional antennas and wireline
Clustering Algorithms for Ad Hoc Wireless Networks”, Ad Hoc and Sensor Networks, edited by
, 2004
"... Abstract. 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 ..."
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Cited by 30 (2 self)
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Abstract. 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. 1. Introduction. In a speculative paper, Kleinrock [32] described ad hoc networking technology as a blend of nomadicity, embeddedness, and ubiquity. In a network of the future, users and computing devices will be able to connect to such a network conveniently and even transparently. Computing and communication capabilities will not only be restricted to standard electronic devices, but every gadget
Distributed Channel Assignment for Multiradio Wireless Networks
, 2006
"... We consider the channel assignment problem for multihop wireless networks in which nodes have multiple interfaces. Given the number of interfaces at each node and available channels in the system, we find a feasible channel assignment to improve network performance. Even when routing is given, findi ..."
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Cited by 24 (3 self)
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We consider the channel assignment problem for multihop wireless networks in which nodes have multiple interfaces. Given the number of interfaces at each node and available channels in the system, we find a feasible channel assignment to improve network performance. Even when routing is given, finding a channel assignment for optimal performance is NPhard. We present the SAFE (Skeleton Assisted partition FrEe) channel assignment scheme, which uses randomized channel assignment in a distributed manner while maintaining network connectivity. SAFE can utilize all independent channels in the system while attempting to distribute edges sharing a particular channel evenly throughout the network. To handle topology change and incremental deployment better, SAFE decouples the channel assignment problem from routing. Our simulation results show that SAFE significantly improves network performance in terms of throughput and delay and is comparable to the best prior centralized scheme that jointly considers routing and channel assignment.
Multicast Time Maximization in Energy Constrained Wireless Networks
, 2003
"... We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energyconstrained (e.g. batteryoperated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a stat ..."
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Cited by 18 (1 self)
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We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energyconstrained (e.g. batteryoperated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static assignment, the power levels of the nodes are set at the beginning and remain unchanged until the nodes are depleted of energy. In a dynamic assignment, the powers can be adjusted during operation. We show