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44
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 111 (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.
The price of being nearsighted
 In SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality o ..."
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Cited by 59 (13 self)
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Achieving a global goal based on local information is challenging, especially in complex and largescale networks such as the Internet or even the human brain. In this paper, we provide an almost tight classification of the possible tradeoff between the amount of local information and the quality of the global solution for general covering and packing problems. Specifically, we give a distributed algorithm using only small messages which obtains an (ρ∆) 1/kapproximation for general covering and packing problems in time O(k 2), where ρ depends on the LP’s coefficients. If message size is unbounded, we present a second algorithm that achieves an O(n 1/k) approximation in O(k) rounds. Finally, we prove that these algorithms are close to optimal by giving a lower bound on the approximability of packing problems given that each node has to base its decision on information from its kneighborhood. 1
Efficient gathering of correlated data in sensor networks
 in Proc. of ACM Intl. symposium on Mobile ad hoc networking and computing, 2005
, 2005
"... In this paper, we design techniques that exploit data correlations in sensor data to minimize communication costs (and hence, energy costs) incurred during data gathering in a sensor network. Our proposed approach is to select a small subset of sensor nodes that may be sufficient to reconstruct data ..."
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Cited by 38 (0 self)
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In this paper, we design techniques that exploit data correlations in sensor data to minimize communication costs (and hence, energy costs) incurred during data gathering in a sensor network. Our proposed approach is to select a small subset of sensor nodes that may be sufficient to reconstruct data for the entire sensor network. Then, during data gathering only the selected sensors need to be involved in communication. The selected set of sensors must also be connected, since they need to relay data to the datagathering node. We define the problem of selecting such a set of sensors as the connected correlationdominating set problem, and formulate it in terms of an appropriately defined correlation structure that captures general data correlations in a sensor network. We develop a set of energyefficient distributed algorithms and competitive centralized heuristics to select a connected correlationdominating set of small size. The designed distributed algorithms can be implemented in an asynchronous communication model, and can tolerate message losses. We also design an exponential (but nonexhaustive) centralized approximation algorithm that returns a solution within O(log n) of the optimal size. Based on the approximation algorithm, we design a class of centralized heuristics that are empirically shown to return nearoptimal solutions. Simulation results over randomly generated sensor networks with both artificially and naturally generated data sets demonstrate the efficiency of the designed algorithms and the viability of our technique – even in dynamic conditions.
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 28 (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
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.
On the locality of distributed sparse spanner construction
 In ACM Press, editor, 27th Annual ACM Symp. on Principles of Distributed Computing (PODC
, 2008
"... The paper presents a deterministic distributed algorithm that, given k � 1, constructs in k rounds a (2k−1, 0)spanner of O(kn 1+1/k)edgesforeverynnode unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k − 2 rounds, and still returns a (2k − 1, 0)spanner with O ..."
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Cited by 16 (7 self)
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The paper presents a deterministic distributed algorithm that, given k � 1, constructs in k rounds a (2k−1, 0)spanner of O(kn 1+1/k)edgesforeverynnode unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k − 2 rounds, and still returns a (2k − 1, 0)spanner with O(kn 1+1/k) edges.) Previous distributed solutions achieving such optimal stretchsize tradeoff either make use of randomization providing performance guarantees in expectation only, or perform in log Ω(1) n rounds, and all require a priori knowledge of n. Based on this algorithm, we propose a second deterministic distributed algorithm that, for every ɛ>0, constructs a (1 + ɛ, 2)spanner of O(ɛ −1 n 3/2)edgesin O(ɛ −1) rounds, without any prior knowledge on the graph. Our algorithms are complemented with lower bounds, which hold even under the assumption that n is known to the nodes. It is shown that any (randomized) distributed algorithm requires k rounds in expectation to compute a (2k − 1, 0)spanner of o(n 1+1/(k−1))edgesfork ∈{2, 3, 5}. It is also shown that for every k>1, any (randomized) distributed algorithm that constructs a spanner with fewer than n 1+1/k+ɛ edges in at most n ɛ expected rounds must stretch some distances by an additive factor of n Ω(ɛ).Inotherwords, while additive stretched spanners with O(n 1+1/k) edges may exist, e.g., for k =2, 3, they cannot be computed distributively in a subpolynomial number of rounds in expectation. Supported by the équipeprojet INRIA “DOLPHIN”. Supported by the ANRproject “ALADDIN”, and the
Fast Distributed Well Connected Dominating Sets for Ad Hoc Networks
, 2004
"... We present the first distributed algorithms for computing connected dominating sets (CDS) for ad hoc networks that break the lineartime barrier. We present two algorithms which require O(\Delta log^2 n)andO(log^2 n) running time respectively, where \Delta is the maximum node degree and n is the siz ..."
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Cited by 14 (0 self)
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We present the first distributed algorithms for computing connected dominating sets (CDS) for ad hoc networks that break the lineartime barrier. We present two algorithms which require O(\Delta log^2 n)andO(log^2 n) running time respectively, where \Delta is the maximum node degree and n is the size of the network. This is a substantial improvement over existing implementations, all of which require \Omega(n) running time.
Distributed Approximation  A Survey
 ACM SIGACT News
"... Abstract Recently considerable progress was achieved in designing efficient distributed apprxoimation algorithms, and in demonstrating hardness of distributed approximation for various problems. In this survey we overview the research in this area and propose several directions for future research. ..."
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Cited by 11 (0 self)
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Abstract Recently considerable progress was achieved in designing efficient distributed apprxoimation algorithms, and in demonstrating hardness of distributed approximation for various problems. In this survey we overview the research in this area and propose several directions for future research.
Distributed algorithms for coloring and domination in wireless ad hoc networks
 In Proc. of FSTTCS
, 2004
"... Abstract. We present fast distributed algorithms for coloring and (connected) dominating set construction in wireless ad hoc networks. We present our algorithms in the context of Unit Disk Graphs which are known to realistically model wireless networks. Our distributed algorithms take into account t ..."
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Cited by 10 (0 self)
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Abstract. We present fast distributed algorithms for coloring and (connected) dominating set construction in wireless ad hoc networks. We present our algorithms in the context of Unit Disk Graphs which are known to realistically model wireless networks. Our distributed algorithms take into account the loss of messages due to contention from simultaneous interfering transmissions in the wireless medium. We present randomized distributed algorithms for (conflictfree) Distance2 coloring, dominating set construction, and connected dominating set construction in Unit Disk Graphs. The coloring algorithm has a time complexity of O( ∆ log 2 n) and is guaranteed to use at most O(1) times the number of colors required by the optimal algorithm. We present two distributed algorithms for constructing the (connected) dominating set; the former runs in time O( ∆ log 2 n) and the latter runs in time O(log 2 n). The two algorithms differ in the amount of local topology information available to the network nodes. Our algorithms are geared at constructing Well Connected Dominating Sets (WCDS) which have certain powerful and useful structural properties such as low size, low stretch and low degree. In this work, we also explore the rich connections between WCDS and routing in ad hoc networks. Specifically, we combine the properties of WCDS with other ideas to obtain the following interesting applications: – An online distributed algorithm for collisionfree, low latency, low redundancy and high throughput broadcasting. – Distributed capacity preserving backbones for unicast routing and scheduling. 1
Constant density spanners for wireless ad hoc networks
 In Proc. of SPAA ’05
, 2005
"... An important problem for wireless ad hoc networks has been to design overlay networks that allow time and energyefficient routing. Many localcontrol strategies for maintaining such overlay networks have already been suggested, but most of them are based on an oversimplified wireless communication ..."
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Cited by 9 (5 self)
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An important problem for wireless ad hoc networks has been to design overlay networks that allow time and energyefficient routing. Many localcontrol strategies for maintaining such overlay networks have already been suggested, but most of them are based on an oversimplified wireless communication model. In this paper, we suggest a model that is much more general than previous models. It allows the path loss of transmissions to significantly deviate from the idealistic unit disk model and does not even require the path loss to form a metric. Also, our model is apparently the first proposed for algorithm design that does not only model transmission and interference issues but also aims at providing a realistic model for physical carrier sensing. Physical carrier sensing is needed so that our protocols do not require any prior information (not even an estimate on the number of nodes) about the