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Journal of the ACM (JACM)
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WDAG '97 Proceedings of the 11th International Workshop on Distributed Algorithms
Heartbeat: A Timeout-Free Failure Detector for Quiescent Reliable Communication
WDAG '97 Proceedings of the 11th International Workshop on Distributed Algorithms
On the Quality of Service of Failure Detectors
DSN '00 Proceedings of the 2000 International Conference on Dependable Systems and Networks (formerly FTCS-30 and DCCA-8)
An optimal algorithm for Monte Carlo estimation
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Probabilistic Analysis of a Group Failure Detection Protocol
WORDS '99 Proceedings of the Fourth International Workshop on Object-Oriented Real-Time Dependable Systems
Toward Maximizing the Quality of Results of Dependent Tasks Computed Unreliably
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DISC'05 Proceedings of the 19th international conference on Distributed Computing
Robust network supercomputing without centralized control
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Robust network supercomputing without centralized control
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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Internet supercomputing is becoming a powerful tool for harnessing massive amounts of computational resources. However in typical master-worker settings the reliability of computation crucially depends on the ability of the master to depend on the computation performed by the workers. Fernandez, Georgiou, Lopez, and Santos [12,13] considered a system consisting of a master process and a collection of worker processes that can execute tasks on behalf of the master and that may act maliciously by deliberately returning fallacious results. The master decides on the correctness of the results by assigning the same task to several workers. The master is charged one work unit for each task performed by a worker. The goal is to design an algorithm that enables the master to determine the correct result with high probability, and at the least possible cost. Fernandez et al. assume that the number of faulty processes or the probability of a process acting maliciously is known to the master. In this paper this assumption is removed. In the setting with n processes and n tasks we consider two different failure models, viz., model ${\mathcal F}_a$, where f-fraction, $0 a priori knowledge of the values of p and f; and model ${\mathcal F}_b$, where at most f-fraction, $0 p, $0 f and p. For model ${\mathcal F}_a$ we provide an algorithm—based on the Stopping Rule Algorithm by Dagum, Karp, Luby, and Ross [10]—that can estimate f and p with (ε,δ)-approximation, for any 0 δε0. This algorithm runs in O(logn) time, O(log2n) message complexity, and O(log2n) task-oriented work and O(nlogn) total-work complexities. We also provide a randomized algorithm for detecting the faulty processes, i.e., identifying the processes that have non-zero probability of failures in model ${\mathcal F}_a$, with task-oriented work O(n), and time O(logn). A lower bound on the total-work complexity of performing n tasks correctly with high probability is shown. Finally, two randomized algorithms to perform n tasks with high probability are given for both failure models with closely matching upper bounds on total-work and task-oriented work complexities, and time O(logn).