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Bounds on the Time to Reach Agreement in the Presence of Timing Uncertainty (Extended Abstract)
, 1991
"... Upper and lower bounds are proved for the real time complexity of the problem of reaching agreement in a distributed network, in the presence of process failures and inexact information about time. It is assumed that the amount of (real) time between any two consecutive steps of any nonfaulty proces ..."
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Cited by 46 (6 self)
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Upper and lower bounds are proved for the real time complexity of the problem of reaching agreement in a distributed network, in the presence of process failures and inexact information about time. It is assumed that the amount of (real) time between any two consecutive steps of any nonfaulty process is at least c1 and at most c2; thus, C = c2/c1 is a measure of the timing uncertainty. It is also assumed that the time for message delivery is at most d. Processes are assumed to fail by stopping, so that process failures can be detected by timeouts. Let T denote...
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 43 (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.
Are WaitFree Algorithms Fast?
, 1991
"... The time complexity of waitfree algorithms in "normal" executions, where no failures occur and processes operate at approximately the same speed, is considered. A lower bound of log n on the time complexity of any waitfree algorithm that achieves approximate agreement among n processes i ..."
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Cited by 39 (11 self)
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The time complexity of waitfree algorithms in "normal" executions, where no failures occur and processes operate at approximately the same speed, is considered. A lower bound of log n on the time complexity of any waitfree algorithm that achieves approximate agreement among n processes is proved. In contrast, there exists a nonwaitfree algorithm that solves this problem in constant time. This implies an (log n) time separation between the waitfree and nonwaitfree computation models. On the positive side, we present an O(log n) time waitfree approximate agreement algorithm; the complexity of this algorithm is within a small constant of the lower bound.
Consensus in the Presence of Timing Uncertainty: Omission and Byzantine Failures
 In Proceedings 10th ACM Symposium on Principles of Distributed Computing
, 1991
"... We consider the time complexity of reaching agreement in a semisynchronous model of distributed systems, in the presence of omission and Byzantine failures. In our semisynchronous model, processes have inexact knowledge about the time to perform certain primitive actions: messages arrive within ti ..."
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Cited by 13 (1 self)
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We consider the time complexity of reaching agreement in a semisynchronous model of distributed systems, in the presence of omission and Byzantine failures. In our semisynchronous model, processes have inexact knowledge about the time to perform certain primitive actions: messages arrive within time d of when they are sent and the time between two consecutive steps of any process is in the known interval [c 1 ; c 2 ]. We use C = c 2 =c 1 as a measure of the timing uncertainty. A simple adaptation of the synchronous lower bound shows that at least time (f + 1)d is required to tolerate f failures; time (f + 1)Cd is sufficient for stopping or omission failures by directly simulating synchronous rounds. By strengthening the algorithm for stopping failures of Attiya, Dwork, Lynch, and Stockmeyer ([1]), we derive an algorithm for omission failures that has minimal dependency on the uncertainty factor C. If fewer than half the processes are faulty then the running time is 4(f + 1)d + Cd, wh...
AND
"... Abstract. Upper and lower bounds are proved for the time complexity of the problem of reaching agreement m a distributed network m the presence of process fwlures and inexact information about time. It is assumed that the amount of (real) time between any two consecutwe steps of any ncmfatrhy proces ..."
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Abstract. Upper and lower bounds are proved for the time complexity of the problem of reaching agreement m a distributed network m the presence of process fwlures and inexact information about time. It is assumed that the amount of (real) time between any two consecutwe steps of any ncmfatrhy process is at least c1 and at most C2; thus, C = cz/cl is a measure of the timing uncertainty. It E also assumed that the time for message dehvery]s at most d. Processes are assumed to fail by stopping, so that process fdures can be detected by timeouts. A straightforward adaptation of an ( ~ + 1)round roundbased agreement algorithm takes time (f + l)Cd If there are f potential faults, while a straightforward mochflcation of the proof that fâ+ 1 rounds are required yields a lower bound of time (~+ 1)d. The frost result of this paper is m agreement algorlthm in which the uncerttimty factor C is only incurred for one round, yielding
The RealTime Cost of Timing Uncertainty: Consensus and Failure Detection
 Laboratory for Computer Science, MIT
, 1991
"... In real distributed systems, processes mayhave only inexact information about the amount of real time needed for primitive operations such as process steps. This thesis studies the effect of this timing uncertainty on the realtime behavior of distributed systems. We consider a semisynchronous mode ..."
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In real distributed systems, processes mayhave only inexact information about the amount of real time needed for primitive operations such as process steps. This thesis studies the effect of this timing uncertainty on the realtime behavior of distributed systems. We consider a semisynchronous model in which the amount of real time between process steps is known to be in the interval #c 1 ;c 2 # and every message is known to be delivered within time d of when it is sent. We use C = c 2 =c 1 as a measure of the timing uncertainty.
Chapter 40 Optimal Time Randomized Consensus Making Resilient Algorithms Fast in Practice*
"... In practice, the design of distributed systems is often geared towards optimizing the time complexity of algorithms in %orrnal â executions, i.e. ones in which at most a small number of failures occur, while at the same time building in safety provisions to protect against many failures. In this ..."
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In practice, the design of distributed systems is often geared towards optimizing the time complexity of algorithms in %orrnal â executions, i.e. ones in which at most a small number of failures occur, while at the same time building in safety provisions to protect against many failures. In this paper we present an optimally fast and highly resilient sharedmemory randomized consensus algorithm that runs in only O(log n) expected time if @or less failures occur, and takes at most O(*) expected tim ~ for any j. Every previously known resilient algorithm required polynomial expected time even if no faults occurred. Using the novel consensus algorithm, we show a method for speedingup resilient algorithms: for any decision problem on n processors, given a highly resilient algorithm as a black box, it modularly generates an algorithm with the same strong properties, that runs in only O(log n) expected time in executions where no failures occur. lThis work was supported by NSF contract CCR