Abstract
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, \(0 < f < \frac{1}{2}\), of the workers provide faulty results with probability \(0 < p < \frac{1}{2}\), given that the master has no a priori knowledge of the values of p and f; and model \({\mathcal F}_b\), where at most f-fraction, \(0 < f < \frac{1}{2}\), of the workers can reply with arbitrary results and the rest reply with incorrect results with probability p, \(0 < p < \frac{1}{2}\), but the master knows the values of 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 < δ< 1 and ε>0. This algorithm runs in O(logn) time, O(log2 n) message complexity, and O(log2 n) 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).
This work is supported in part by the NSF Grants 0121277 and 0311368.
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Distributed .net, http://www.distributed.net/
Internet primenet server, http://mersenne.org/ips/stats.html
Seti@home, http://setiathome.ssl.berkeley.edu/
Aguilera, M.K., Chen, W., Toueg, S.: Heartbeat: a timeout-free failure detector for quiescent reliable communication. In: Mavronicolas, M. (ed.) WDAG 1997. LNCS, vol. 1320, pp. 126–140. Springer, Heidelberg (1997)
Almeida, C., Verissimo, P.: Timing failure detection and real-time group communication in real-time systems. In: Proceedings of 8th Euromicro Workshop on Real-Time Systems (June 1996)
Bollo, R., Narzul, J.P.L., Raynal, M., Tronel, F.: Probabilistic analysis of a group failure detection protocol. In: Proceedings of 4th International Workshop on Object-Oriented Real-Time Dependable Systems(WORDS 1999) (January 1999)
Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. Journal of the ACM 43(2), 225–267 (1996)
Chen, W., Toueg, S., Aguilera, M.K.: On the quality of service of failure detectors. In: Proceedings of 30th International Conference on Dependable Systems and Networks (ICDSN/FTCS-30) (June 2000)
Chlebus, B.S., De Prisco, R., Shvartsman, A.A.: Performing tasks on restartable message-passing processors. In: Mavronicolas, M. (ed.) WDAG 1997. LNCS, vol. 1320, pp. 96–110. Springer, Heidelberg (1997)
Dagum, P., Karp, R.M., Luby, M., Ross, S.: An optimal algorithm for monte carlo estimation. In: Proceedings of the Foundations of Computer Science, pp. 142–149 (1995)
Dwork, C., Halpern, J.Y., Waarts, O.: Performing work efficiently in the presence of faults. In: Proceedings of the eleventh annual ACM symposium on Principles of distributed computing, pp. 91–102 (1992)
Fernández, A., Georgiou, C., López, L., Santos, A.: Reliably executing tasks in the presence of malicious processors. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 490–492. Springer, Heidelberg (2005)
Fernandez, A., Georgiou, C., Lopez, L., Santos, A.: Reliably executing tasks in the presence of malicious processors. Technical Report Numero 9 (RoSaC-2005-9), Grupo de Sistemas y Comunicaciones, Universidad Rey Juan Carlos (2005), http://gsyc.escet.urjc.es/publicaciones/tr/RoSaC-2005-9.pdf
Gao, L., Malewicz, G.: Toward maximizing the quality of results of dependent tasks computed unreliably. Theory of Computing Systems (to appear); preliminary version OPODIS 2004
Karp, R.M.: Probabilistic recurrence relations. Journal of the Association for Computing Machinery 41(6), 1136–1150 (1994)
Kedem, Z.M., Palem, K.V., Raghunathan, A., Spirakis, P.: Combining tentative and definite executions for dependable parallel computing, pp. 381–390 (1991)
Konwar, K.M., Rajasekaran, S., Shvartsman, A.A.: Robust network supercomputing with malicious processes (2006), http://www.cse.uconn.edu/~kishori/KRS2006.pdf
Korpela, E., Werthimer, D., Anderson, D., Cobb, J., Lebofsky, M.: Seti@home - massively distributed computing for seti. Computing in Science & Enginering 3(1) (2001)
Martel, C., Subramonian, R.: On the complexity of certified write-all algorithms. Journal of Algorithms 16(3), 361–387 (1994)
Paquette, M., Pelc, A.: Optimal decision strategies in byzantine environments. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 245–254. Springer, Heidelberg (2004)
De. Prisco, R., Mayer, A., Yung, M.: Time-optimal message-efficientwork performance in the presence of faults. In: Proceedings of the 13th ACM Symp. Principles of Distributed Computing, pp. 161–172 (1994)
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Konwar, K.M., Rajasekaran, S., Shvartsman, A.A. (2006). Robust Network Supercomputing with Malicious Processes. In: Dolev, S. (eds) Distributed Computing. DISC 2006. Lecture Notes in Computer Science, vol 4167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11864219_33
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