Abstract
This paper presents a study of a distributed cooperation problem under the assumption that processors may not be able to communicate for a prolonged time. The problem for n processors is defined in terms of the tasks that need to be performed efficiently and that are known to all processors. The results of this study characterize the ability of the processors to schedule their work so that when some processors establish communication, the wasted (redundant) work these processors have collectively performed prior to that time is controlled. The lower bound for wasted work presented here shows that for any set of schedules there are two processors such that when they complete t 1 and t 2 tasks respectively the number of redundant tasks is Ω(tit2/t). For n = t and for schedules longer than \( \mathbb{E}\) , the number of redundant tasks for two or more processors must be at least 2. The upper bound on pairwise waste for schedules of length y/n is shown to be 1. Our efficient deterministic sched- -ule construction is motivated by design theory. To obtain linear length schedules, a novel deterministic and efficient construction is given. This construction has the property that pairwise wasted work increases grace- -fully as processors progress through their schedules. Finally our analysis of a random scheduling solution shows that with high probability pair- wise waste is well behaved at all times: specifically, two processors having completed t 1 and t 2 tasks, respectively, are guaranteed to have no more than t¨Jt + A redundant tasks, where A = O(logn + √t1t2/t√logn).
This work was supported by NSF Grant CCR-9988304 and a grant from AFOSR.
The work of the third author was supported by a NSF Career Award
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References
Alon, N., Spencer, J. H.: The probabilistic method. John Wiley & Sons Inc. New York (1992). With an appendix by Paul Erdös, A Wiley-Interscience Publication
Aumann, Y., Rabin, M.O.: Clock Construction in Fully Asynchronous Parallel Systems and PRAM Simulation. Foundations of Comp. Sc. (1993) 147–156
Chlebus, B.S., De Prisco, R., Shvartsman, A.A.: Performing Tasks on Restartable Message-Passing Processors. Intl Workshop on Distributed Algorithms. Lecture Notes in Computer Science, Vol. 1320. (1997) 96–110
Colbourn, C. J., van Oorschot, P. C: Applications of Combinatorial Designs in Computer Science. ACM Computing Surveys, Vol. 21. 2 (1989)
De Prisco, R., Mayer, A., Yung, M.: Time-Optimal Message-Efficient Work Per-formance in the Presence of Faults. ACM Symposium on Principles of Distributed Computing. (1994) 161–172
Dolev, S., Segala, R., Shvartsman, A.A.: Dynamic Load Balancing with Group Communication. Intl Colloquium on Structural Information and Communication Complexity. (1999) 111–125
Dwork, C, Halpern, J., Waarts, O.: Performing Work Efficiently in the Presence of Faults. SIAM J. on Computing, Vol. 27 5. (1998) 1457–1491
Georgiades, S., Mavronicolas, M., Spirakis, P.: Optimal, Distributed Decision-Making: The Case of No Communication. Intl Symposium on Fundamentals of Computation Theory. (1999) 293–303
Georgiou, Ch., Shvartsman A: Cooperative Computing with Fragmentable and Mergeable Groups. International Colloquium on Structure of Information and Communication Complexity. (2000) 141–156
Hughes, D.R., Piper, F.C.: Design Theory. Cambridge University Press (1985)
Ireland, K., Rosen, M.: A Classical Introdiction to Modern Number Theory. 2nd edn. Springer-Verlag (1990)
Kanellakis, P.C., Shvartsman, A.A.: Fault-Tolerant Parallel Computation. Kluwer Academic Publishers (1997)
Kedem, Z.M., Palem, K.V., Rabin, M.O., Raghunathan, A.: Efficient Program Transformations for Resilient Parallel Computation via Randomization. ACM Symp. on Theory of Comp. (1992) 306–318
Knuth, D.E.: The Art of Computer Programming. 2nd edn. Addison-Wesley Pub-lishing Company, Vol. 2. (1981)
Malewicz, G., Russell, A., Shvartsman, A.A.: Distributed Cooperation in the Absence of Communication. Technical Report MIT-LCS-TR-804 available at http://theory.lcs.mit.edu/~alex/mrsTR.ps. (Also: Brief announcement. ACM Sym-posium on Principles of Distributed Computing. (2000))
Martel, C, Park, A., Subramonian, R.: Work-optimal asynchronous algorithms for shared memory parallel computer. SIAM J. on Computing, Vol. 21 6 (1992) 1070–1099
Miller, G.L.: Riemann’s Hypothesis and Tests for Primality. Journal of Computer and Systems Sciences, Vol. 13 (1976) 300–317
Papadimitriou, C.H., Yannakakis, M.: On the value of information in distributed decision-making. ACM Symp. on Principles of Dist. Computing. (1991) 61–64
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Malewicz, G.G., Russell, A., Shvartsman, A.A. (2000). Distributed Cooperation During the Absence of Communication. In: Herlihy, M. (eds) Distributed Computing. DISC 2000. Lecture Notes in Computer Science, vol 1914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40026-5_8
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