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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 44 (4 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.
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 43 (5 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...
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 is proved. ..."
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Cited by 42 (12 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...