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20
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
Fast Broadcasting and Gossiping in Radio Networks
, 2000
"... We establish an O(n log² n) upper bound on the time for deterministic distributed broadcasting in multihop radio networks with unknown topology. This nearly matches the known lower bound of n log n). The fastest previously known algorithm for this problem works in time O(n 3=2 ). Using our broa ..."
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Cited by 87 (6 self)
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We establish an O(n log² n) upper bound on the time for deterministic distributed broadcasting in multihop radio networks with unknown topology. This nearly matches the known lower bound of n log n). The fastest previously known algorithm for this problem works in time O(n 3=2 ). Using our broadcasting algorithm, we develop an O(n 3=2 log 2 n) algorithm for gossiping in the same network model.
A parallel algorithmic version of the local lemma
, 1991
"... The Lovász Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for ..."
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Cited by 60 (10 self)
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The Lovász Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of loosing a little in the estimates. His method does not seem to be parallelizable. Here we modify his technique and achieve an algorithmic version that can be parallelized, thus obtaining deterministic NC 1 algorithms for several interesting algorithmic problems.
Broadcast in Radio Networks
, 1995
"... We show that for any radio network there exists a schedule of a broadcast whose time is O(D + log 5 (n)), where D is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D = \Omega\Gamma115 5 n).) We present a (centralized) polynomial time algorit ..."
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Cited by 54 (4 self)
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We show that for any radio network there exists a schedule of a broadcast whose time is O(D + log 5 (n)), where D is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D = \Omega\Gamma115 5 n).) We present a (centralized) polynomial time algorithm that given a network and a source, outputs a schedule for broadcasting the message from the source to the rest of the network. 1 Introduction The importance of radio communication networks is increasing. The applications of radio communications has shifted from the traditional military applications to civilian applications such as cellular phones and wireless local area networks (LAN). One of the main advantages of radio communication is the the relative small investment in a rigid infrastructure. In addition, radio networks allows for mobile users, a feature which is crucial in many applications. One of the basic tasks in a radio networks is broadcast. Broadcast is used for locating a ...
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...
Computation in Noisy Radio Networks
 in Proc. 9th Ann. ACMSIAM Symp. on Discrete Algorithms
"... In this paper we examine noisy radio (broadcast) networks in which every bit transmitted has a certain probability to be flipped. Each processor has some initial input bit, and the goal is to compute a function of the initial inputs. In this model we show a protocol to compute any threshold function ..."
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Cited by 30 (0 self)
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In this paper we examine noisy radio (broadcast) networks in which every bit transmitted has a certain probability to be flipped. Each processor has some initial input bit, and the goal is to compute a function of the initial inputs. In this model we show a protocol to compute any threshold function using only a linear number of transmissions. 1 Introduction The influence of noise (or faults) on the complexity of computation was studied in many contexts. In particular people were interested in random noise. In a typical such scenario, it is assumed that the outcome of each operation is noisy with some fixed probability p and all the faults are independent. Usually, if t is the number of operations performed by the computation, then by repeating each operation O(log t) times and taking the majority of the results, one can ensure a constant probability of error at the cost of O(t log t) operations. It is desirable however to obtain a cost of O(t) (i.e., increase only by a constant fa...
Logarithmic inapproximability of the radio broadcast problem
 Journal of Algorithms
, 2004
"... We show that the radio broadcast problem is Ω(log n)inapproximable unless NP ⊆ BPTIME(n O(loglog n)). This is the first result on the hardness of approximation of this problem. Our reduction is based on the reduction from the LabelCover problem to the Set Cover problem due to Lund and Yannakakis [ ..."
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Cited by 17 (0 self)
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We show that the radio broadcast problem is Ω(log n)inapproximable unless NP ⊆ BPTIME(n O(loglog n)). This is the first result on the hardness of approximation of this problem. Our reduction is based on the reduction from the LabelCover problem to the Set Cover problem due to Lund and Yannakakis [LY94], and uses some new ideas.
A randomized algorithm for gossiping in radio networks
 NETWORKS
, 2004
"... We present an O(n log 4 n)time randomized algorithm for gossiping in radio networks with unknown topology. This is the first algorithm for gossiping in this model whose running time is only a polylogarithmic factor away from the optimum. The fastest previously known (deterministic) algorithm for th ..."
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Cited by 15 (2 self)
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We present an O(n log 4 n)time randomized algorithm for gossiping in radio networks with unknown topology. This is the first algorithm for gossiping in this model whose running time is only a polylogarithmic factor away from the optimum. The fastest previously known (deterministic) algorithm for this problem works in time O(n 3/2 log 2 n).