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61
On the Cost of FaultTolerant Consensus When There Are No Faults  A Tutorial
, 2001
"... We consider the consensus problem in asynchronous models enriched with unreliable failure detectors or partial synchrony, where processes can crash or links may fail by losing messages. ..."
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Cited by 68 (8 self)
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We consider the consensus problem in asynchronous models enriched with unreliable failure detectors or partial synchrony, where processes can crash or links may fail by losing messages.
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 47 (5 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
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 40 (17 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 &quot;anonymous &quot; 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.
Tight bounds for asynchronous randomized consensus
 In STOC ’07: Proceedings of the thirtyninth annual ACM symposium on Theory of computing
, 2007
"... A distributed consensus algorithm allows n processes to reach a common decision value starting from individual inputs. Waitfree consensus, in which a process always terminates within a finite number of its own steps, is impossible in an asynchronous sharedmemory system. However, consensus becomes ..."
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Cited by 21 (5 self)
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A distributed consensus algorithm allows n processes to reach a common decision value starting from individual inputs. Waitfree consensus, in which a process always terminates within a finite number of its own steps, is impossible in an asynchronous sharedmemory system. However, consensus becomes solvable using randomization when a process only has to terminate with probability 1. Randomized consensus algorithms are typically evaluated by their total step complexity, which is the expected total number of steps taken by all processes. This work proves that the total step complexity of randomized consensus is Θ(n 2) in an asynchronous shared memory system using multiwriter multireader registers. The bound is achieved by improving both the lower and the upper bounds for this problem. In addition to improving upon the best previously known result by a factor of log 2 n, the lower bound features a greatly streamlined proof. Both goals are achieved through restricting attention to a set of layered executions and using an isoperimetric inequality for analyzing their behavior. The matching algorithm decreases the expected total step complexity by a log n factor, by leveraging the multiwriting capability of the shared registers. Its correctness proof is facilitated by viewing each execution of the algorithm as a stochastic process and applying Kolmogorov’s inequality.
Chasing the weakest system model for implementing and consensus. Brief Annoucement
 Proc. 8th Int’l Symp. on Stabilization, Safety and Security in Distributed Systems (SSS’06), SpringerVerlag LNCS #4280
, 2006
"... Abstract — Aguilera et al. and Malkhi et al. have presented two system models, which are weaker than all previously proposed models where the eventual leader election oracle Ω can be implemented and thus also consensus can be solved. The former model assumes unicast steps and at least one correct ..."
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Cited by 20 (2 self)
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Abstract — Aguilera et al. and Malkhi et al. have presented two system models, which are weaker than all previously proposed models where the eventual leader election oracle Ω can be implemented and thus also consensus can be solved. The former model assumes unicast steps and at least one correct process with f outgoing eventually timely links, whereas the latter assumes broadcast steps and at least one correct process with f bidirectional but moving eventually timely links. Consequently, those models are incomparable. In this paper, we show that Ω can also be implemented in a system with at least one process with f outgoing moving eventually timely links, assuming either unicast or broadcast steps. It seems to be the weakest system model that allows to solve consensus via Ωbased algorithms known so far. We also provide matching lower bounds for the communication complexity of Ω in this model, which are based on an interesting “stabilization property ” of infinite runs. Those results reveal a fairly high price to be paid for the further relaxation of synchrony properties.
Coordinated Consensus in Dynamic Networks
"... We study several variants of coordinated consensus in dynamic networks. We assume a synchronous model, where the communication graph for each round is chosen by a worstcase adversary. The network topology is always connected, but can change completely from one round to the next. The model captures ..."
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Cited by 19 (1 self)
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We study several variants of coordinated consensus in dynamic networks. We assume a synchronous model, where the communication graph for each round is chosen by a worstcase adversary. The network topology is always connected, but can change completely from one round to the next. The model captures mobile and wireless networks, where communication can be unpredictable. In this setting we study the fundamental problems of eventual, simultaneous, and ∆coordinated consensus, as well as their relationship to other distributed problems, such as determining the size of the network. We show that in the absence of a good initial upper bound on the size of the network, eventual consensus is as hard as computing deterministic functions of the input, e.g., the minimum or maximum of inputs to the nodes. We also give an algorithm for computing such functions that is optimal in every execution. Next, we show that simultaneous consensus can never be achieved in less than n−1 rounds in any execution, where n is the size of the network; consequently, simultaneous consensus is as hard as computing an upper bound on the number of nodes in the network. For ∆coordinated consensus, we show that if the ratio between nodes with input 0 and input 1 is bounded away from 1, it is possible to decide in timen−Θ ( √ n∆), where∆bounds the time from the first decision until all nodes decide. If the dynamic graph has diameterD, the time to decide ismin{O(nD/∆),n−Ω(n∆/D)}, even if D is not known in advance. Finally, we show that (a) there is a dynamic graph such that for every input, no node can decide before timen−O( ∆ 0.28 n 0.72); and (b) for any diameterD=O(∆), there is an execution with diameter D where no node can decide before time Ω(nD/∆). To our knowledge, our work constitutes the first study of ∆coordinated consensus in general graphs.
Consensus and collision detectors in radio networks
, 2008
"... We consider the faulttolerant consensus problem in radio networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop radios networks, where all nodes are located within broadcast range of each other. In a novel break from existing ..."
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Cited by 15 (8 self)
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We consider the faulttolerant consensus problem in radio networks with crashprone nodes. Specifically, we develop lower bounds and matching upper bounds for this problem in singlehop radios networks, where all nodes are located within broadcast range of each other. In a novel break from existing work, we introduce a collisionprone communication model in which each node may lose an arbitrary subset of the messages sent by its neighbors during each round. This model is motivated by 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
Rendezvous of mobile agents in unknown graphs with faulty links
 In Proc. of Distributed Computing, 21st International Conference (DISC 2007), Lecture Notes in Computer Science
, 2007
"... A group of mobile agents wandering among the nodes of a network have to gather together in a single node of the graph; This problem known as the Rendezvous problem has been studied extensively but only for networks that are safe or faultfree. In this paper, we consider the case when some of the edg ..."
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Cited by 14 (11 self)
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A group of mobile agents wandering among the nodes of a network have to gather together in a single node of the graph; This problem known as the Rendezvous problem has been studied extensively but only for networks that are safe or faultfree. In this paper, we consider the case when some of the edges in the network are dangerous or faulty such that any agent entering one of these nodes would be destroyed. Our objective is to minimize the number of agents that are destroyed and achieve rendezvous of all the surviving agents. We determine under what conditions this is possible and present algorithms for achieving rendezvous in such cases. Our algorithms are for arbitrary networks with an arbitrary number of dangerous channels; thus our model is a generalization of the case where all the dangerous channels lead to single node, called the Black Hole. We do not assume prior knowledge of the network topology; In fact, we show that knowledge of only a “tight ” bound on the network size is sufficient for solving the problem. 1
Improving Fast Paxos: being optimistic with no overhead.
 In Pacific Rim Dependable Computing (PRDC),
, 2006
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Agreement in synchronous networks with ubiquitous faults
, 2007
"... In this paper we are interested in synchronous distributed systems subject to transient and ubiquitous failures. This includes systems where failures will occur on any communication link, systems where every processor will experience at one time or another send or receive failure, etc., and, followi ..."
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Cited by 13 (1 self)
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In this paper we are interested in synchronous distributed systems subject to transient and ubiquitous failures. This includes systems where failures will occur on any communication link, systems where every processor will experience at one time or another send or receive failure, etc., and, following a failure, normal functioning resuming after a finite time. Notice that these cases cannot be handled by the traditional component failure models. The model we use is the communication failure model, also called the transmission failure or dynamic faults or mobile faults model. Using this model, we study the fundamental problem of agreement in synchronous networks of arbitrary topology with ubiquitous faults. We establish bounds on the number of dynamic faults that make any nontrivial form of agreement (even strong majority) impossible; in turn, these bounds express connectivity requirements that must be met to achieve any meaningful form of agreement. We also provide, constructively, bounds on the number of dynamic faults in spite of which any nontrivial form of agreement (even unanimity) is possible. These bounds are shown to be tight for a large class of networks, which includes hypercubes, toruses, rings, and complete graphs; incidentally, we close the existing gap between possibility and impossibility of nontrivial agreement in complete graphs in the presence of dynamic Byzantine faults. None of these results is derivable in the component failure models; in particular, all our possibility results hold in situations for which those models indicate impossibility.