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87
What Cannot Be Computed Locally!
 In Proceedings of the 23 rd ACM Symposium on the Principles of Distributed Computing (PODC
, 2004
"... We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors# /k) and # /k) for some constant c, where n and # denote the number ..."
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Cited by 99 (26 self)
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We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors# /k) and # /k) for some constant c, where n and # denote the number of nodes and the largest degree in the graph. The number of rounds required in order to achieve a constant or even only a polylogarithmic approximation ratio is at log n/ log log n) and#1 #/ log log #). By a simple reduction, the latter lower bounds also hold for the construction of maximal matchings and maximal independent sets.
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 99 (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 84 (7 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.
Combination Can Be Hard: Approximability of the Unique Coverage Problem
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms
, 2006
"... Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we pro ..."
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Cited by 61 (2 self)
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Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we prove O(1 / logoe n) inapproximability for some constant oe = oe("). We also prove O(1 / log1/3 " n) inapproximability, forany "> 0, assuming that refuting random instances of 3SAT is hard on average; and prove O(1 / log n)inapproximability under a plausible hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish an \Omega (1 / log n)approximation algorithm, even for a moregeneral (budgeted) setting, and obtain an \Omega (1 / log B)approximation algorithm when every set hasat most B elements. We also show that our inapproximability results extend to envyfree pricing, animportant problem in computational economics. We describe how the (budgeted) unique coverage problem, motivated by realworld applications, has close connections to other theoretical problemsincluding max cut, maximum coverage, and radio broadcasting. 1 Introduction In this paper we consider the approximability of the following natural maximization analog of set cover: Unique Coverage Problem. Given a universe U = {e1,..., en} of elements, and given a collection S = {S1,..., Sm} of subsets of U. Find a subcollection S0 ` S to maximize the number of elements that are uniquely covered, i.e., appear in exactly one set of S 0.
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.
Initializing Newly Deployed Ad Hoc and Sensor Networks
 in Proceedings of 10 th Annual International Conference on Mobile Computing and Networking (MOBICOM
, 2004
"... A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi ..."
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Cited by 49 (14 self)
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A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed e#ciently. Our algorithm e#ciently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.
Centralized Broadcast in Multihop Radio Networks
, 2003
"... We show that for any radio network there exists a schedule of a broadcast whose time is O(D+log n),whereD is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D n).) We present a centralized randomized polynomial time algorithm that given a ..."
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Cited by 43 (0 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 n),whereD is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D n).) We present a centralized randomized 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.
Broadcast in Radio Networks Tolerating Byzantine Adversarial Behavior
 In PODC ’04: Proceedings of the twentythird annual ACM symposium on Principles of distributed computing
, 2004
"... Much work has focused on the Byzantine Generals (or secure broadcast) problem in the standard model in which pairwise communication is available between all parties in the network. Some research has also explored the problem when pairwise channels exist only between selected pairs of players, or und ..."
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Cited by 42 (2 self)
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Much work has focused on the Byzantine Generals (or secure broadcast) problem in the standard model in which pairwise communication is available between all parties in the network. Some research has also explored the problem when pairwise channels exist only between selected pairs of players, or under the assumption of \kcast channels" shared by all subsets of players of size k. However, none of these models are appropriate for radio networks in which a player can communicate only by multicasting a message which is then received by all players within some radius r (i.e., the neighbors of the transmitting node). Yet, as far as we are aware, obtaining secure broadcast in radio networks in the presence of a Byzantine adversary has not been studied before. This paper corrects this omission, and provides the rst analysis of secure broadcast in radio networks for the case of Byzantine adversaries. We note that secure broadcast is impossible in the presence of an omnipotent adversary. To bypass this barrier, we make the following assumption: there exists a pre xed schedule for players to communicate and everyone (including corrupted ones) adheres to this schedule. Under this assumption, we give a simple broadcast protocol which is provably secure whenever the adversary corrupts at most 2 +1) 3 neighbors (roughly a 1=4 fraction) of any honest player. On the other hand, we show that it is impossible to achieve secure broadcast when the adversary corrupts d 2 r(2r + 1)e (roughly a 1= fraction) neighbors of any honest player.
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 39 (12 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...
Maximal Independent Sets in Radio Networks
"... We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with ..."
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Cited by 33 (7 self)
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We study the distributed complexity of computing a maximal independent set (MIS) in radio networks with completely unknown topology, asynchronous wakeup, and no collision detection mechanism available. Specifically, we propose a novel randomized algorithm that computes a MIS in time O(log 2 n) with high probability, where n is the number of nodes in the network. This significantly improving on the best previously known solutions. A lower bound of Ω(log 2 n / log log n) given in [11] implies that our algorithm’s running time is close to optimal. Our result shows that the harsh radio network model imposes merely an additional O(log n) factor compared to Luby’s MIS algorithm in the message passing model. This has important implications in the context of ad hoc and sensor networks whose characteristics are closely captured by the radio network model.