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42
An Ω(D log(N/D)) Lower Bound for Broadcast in Radio Networks
 SIAM Journal on Computing
, 1998
"... Abstract. We show that for any randomized broadcast protocol for radio networks, there exists a network in which the expected time to broadcast a message is Ω(D log(N/D)), where D is the diameter of the network and N is the number of nodes. This implies a tight lower bound of Ω(D log N) for any D ≤ ..."
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Cited by 112 (4 self)
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Abstract. We show that for any randomized broadcast protocol for radio networks, there exists a network in which the expected time to broadcast a message is Ω(D log(N/D)), where D is the diameter of the network and N is the number of nodes. This implies a tight lower bound of Ω(D log N) for any D ≤ N 1−ε, where ε>0 is any constant.
Broadcasting algorithms in radio networks with unknown topology
 In Proc. of FOCS
, 2003
"... In this paper we present new randomized and deterministic algorithms for the classical problem of broadcasting in radio networks with unknown topology. We consider directed nnode radio networks with specified eccentricity D (maximum distance from the source node to any other node). In a seminal wor ..."
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Cited by 102 (1 self)
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In this paper we present new randomized and deterministic algorithms for the classical problem of broadcasting in radio networks with unknown topology. We consider directed nnode radio networks with specified eccentricity D (maximum distance from the source node to any other node). In a seminal work on randomized broadcasting, BarYehuda et al. presented an algorithm that for any nnode radio network with eccentricity D completes the broadcasting in O(D log n + log 2 n) time, with high probability. This result is almost optimal, since as it has been shown by Kushilevitz and Mansour and Alon et al., every randomized algorithm requires Ω(D log(n/D)+log 2 n) expected time to complete broadcasting. Our first main result closes the gap between the lower
Multiple Communication in MultiHop Radio Networks
 SIAM Journal on Computing
, 1993
"... Two tasks of communication in a multihop synchronous radio network are considered: pointtopoint communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowled ..."
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Cited by 69 (1 self)
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Two tasks of communication in a multihop synchronous radio network are considered: pointtopoint communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowledge messages deterministically. Let n, D, and Δ be the number of nodes, the diameter and the maximum degree of our network, respectively. Both protocols require a setup phase in which a BFS tree is constructed. This phase takes O ((n + Dlogn)logΔ) time. After the setup, k pointtopoint transmissions require O ((k +D)logΔ) time on the average. Therefore the network allows a new transmission every O (logΔ) time slots. Also, k broadcasts require an average of O ((k +D)logΔlogn) time. Hence the average throughput of the network is a broadcast every O(logΔlogn) time slots. Both protocols pipeline the messages along the BFS tree. They are always successful on the graph spanned by the BFS tree. Their probabilistic behavior refers only to the running time. Using the above protocols the ranking problem is solved in O (nlognlogΔ) time. The performance analysis of both protocols constitutes a new application of queueing theory.
Probabilistic Algorithms for the Wakeup Problem in SingleHop Radio Networks
 In Proceedings of 13 th Annual International Symposium on Algorithms and Computation (ISAAC
, 2002
"... We consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake ..."
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Cited by 54 (0 self)
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We consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake all the processors up with probability 1e in each of these eight models. In [11] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/logn). We also show logarithmic or polylogarithmic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.
Deterministic Radio Broadcasting
, 2000
"... We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are ..."
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Cited by 44 (11 self)
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We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are not assumed to know their neighbors, nor the size of the network, they are aware only of their individual identifying numbers. If more than one message is delivered to a node in a step then the node cannot hear any of them. Nodes cannot distinguish between such collisions and the case when no messages have been delivered in a step. The fastest previously known deterministic algorithm for deterministic distributed broadcasting in unknown radio networks was presented in [6], it worked in time O(n 11=6 ). We develop three new deterministic distributed algorithms. Algorithm A develops further the ideas of [6] and operates in time O(n 1:77291 ) = O(n 9=5 ), for general networks...
Consensus and collision detectors in wireless ad hoc networks
 In PODC
, 2005
"... Abstract In this study, we consider the faulttolerant consensus problem in wireless ad hoc networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop wireless networks, where all nodes are located within broadcast range of each oth ..."
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Cited by 42 (19 self)
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Abstract In this study, we consider the faulttolerant consensus problem in wireless ad hoc networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop wireless networks, where all nodes are located within broadcast range of each other. In a novel break from existing work, we introduce a highly unpredictable communication model in which each node may lose an arbitrary subset of the messages sent by its neighbors during each round. We argue that this model better matches behavior observed in empirical studies of these networks. To cope with this communication unreliability we augment nodes with receiverside collision detectors and present a new classification of these detectors in terms of accuracy and completeness. This classification is motivated by practical realities and allows us to determine, roughly speaking, how much collision detection capability is enough to solve the consensus problem efficiently in this setting. We consider ten different combinations of completeness and accuracy properties in total, determining for each whether consensus is solvable, and, if it is, a lower bound on the number of rounds required. Furthermore, we distinguish anonymous and nonanonymous protocolswhere "anonymous " implies that devices do not have unique identifiersdetermining what effect (if any) this extra information has on the complexity of the problem. In all relevant cases, we provide matching upper bounds. Our contention is that the introduction of (possibly weak) receiverside collision detection is an important approach to reliably solving problems in unreliable networks. Our results, derived in a realistic network model, provide important feedback to ad hoc network practitioners regarding what hardware (and lowlayer software) collision detection capability is sufficient to facilitate the construction of reliable and faulttolerant agreement protocols for use in realworld deployments.
Uniform Leader Election Protocols for Radio Networks
 In ICPP ’02: Proceedings of the 2001 International Conference on Parallel Processing
, 2001
"... A radio network is a distributed system with no central arbiter, consisting of radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the sta ..."
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Cited by 23 (0 self)
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A radio network is a distributed system with no central arbiter, consisting of radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the station as leader. A leader election protocol is said to be uniform if in each time slot every station transmits with the same probability. In a seminal paper Willard [9] presented a uniform leader election protocol for singlechannel singlehop radio stations terminating in expected time slots. It was open whether Willard's protocol featured the same time performance with "high probability". We propose a uniform leader election protocol that terminates, with probability exceeding for every , in ! " time slots. We also prove that for every $#&%(')*,+ , in order to ensure termination with probability exceeding , Willard's protocol must take  2 time slots. Finally, we provide simulation results that show that our leader election outperforms Willard's leader election protocol in practice. 1
Extremal properties of threedimensional sensor networks with applications
 IEEE Transactions on Mobile Computing
"... In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in threedimensional sensor networks. As in other largescale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a cri ..."
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Cited by 21 (1 self)
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In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in threedimensional sensor networks. As in other largescale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that n nodes, each capable of sensing events within a radius of r, are randomly and uniformly distributed in a 3dimensional region R of volume V, how large must the sensing range rSense be to ensure a given degree of coverage of the region to monitor? For a given transmission range rTrans, what is the minimum (resp. maximum) degree of the network? What is then the typical hopdiameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks. Keywords Sensor networks, ad hoc networks; coverage, connectivity; hopdiameter; minimum/maximum degrees; transmitting/sensing ranges; analytical methods; energy consumption; topology control. I.
Randomized Initialization Protocols for Ad Hoc Networks
 IEEE Transactions on Parallel and Distributed Systems
, 2000
"... AbstractÐAd hoc networks are selforganizing entities that are deployed on demand in support of various events including collaborative computing, multimedia classroom, disasterrelief, searchandrescue, interactive mission planning, and law enforcement operations. One of the fundamental tasks that ..."
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Cited by 20 (2 self)
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AbstractÐAd hoc networks are selforganizing entities that are deployed on demand in support of various events including collaborative computing, multimedia classroom, disasterrelief, searchandrescue, interactive mission planning, and law enforcement operations. One of the fundamental tasks that have to be addressed when setting up an ad hoc network (AHN, for short) is initialization. This involves assigning each of the n stations in the AHN a distinct ID number (e.g., a local IP address) in the range from 1 to n. Our main contribution is to propose efficient randomized initialization protocols for AHNs. We begin by showing that if the number 1 n of stations is known beforehand, an nstation, singlechannel AHN can be initialized with probability exceeding 1 n,inen‡ p O … n log n† time slots, regardless of whether the AHN has collision detection capability. We then go on to show that even if n is not 1 known in advance, an nstation, singlechannel AHN with collision detection can be initialized with probability exceeding 1 n,in
M.: On randomized broadcasting and gossiping in radio networks
 COCOON 2002. LNCS
, 2002
"... Abstract. This paper has two parts. In the first part we give an alternative (and much simpler) proof for the best known lower bound of Ω(D log (N/D)) timesteps for randomized broadcasting in radio networks with unknown topology. In the second part we give an O(N log 3 N)time randomized algorithm f ..."
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Cited by 19 (0 self)
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Abstract. This paper has two parts. In the first part we give an alternative (and much simpler) proof for the best known lower bound of Ω(D log (N/D)) timesteps for randomized broadcasting in radio networks with unknown topology. In the second part we give an O(N log 3 N)time randomized algorithm for gossiping in such radio networks. This is an improvement over the fastest previously known algorithm that works in time O(N log 4 N). 1