ABSTRACT
The problem of cooperatively performing a set of t tasks in a decentralized setting where the computing medium is subject to failures is one of the fundamental problems in distributed computing. The setting with partitionable networks is especially challenging, as algorithmic solutions must accommodate the possibility that groups of processors become disconnected (and, perhaps, reconnected) during the computation. The efficiency of task-performing algorithms is often assessed in terms of their work: the total number of tasks, counting multiplicities, performed by all of the processors during the computation. In general, an adversary that is able to partition the network into g components can cause any task-performing algorithm to have work Ω(t•g) even if each group of processors performs no more than the optimal number of Θ(t) tasks.Given such pessimistic lower bounds, and in order to understand better the practical implications of performing work in partitionable settings, we study distributed work-scheduling andpursue a competitiveanalysis. Specifically, we study asimple randomized scheduling algorithm for p asynchronous processors, connected by a dynamically changing communication medium, to complete t known tasks. We compare the performance of the algorithm against that of an "off-line" algorithm with full knowledge of the future changes in the communication medium. We describe a notion of computation width, which associates a natural number with a history of changes in the communication medium, and show both upper and lower bounds on competitiveness in terms of this quantity. Specifically, we show that a simple randomized algorithm obtains the competitive ratio (1+cw/e), where cw is computation width; we then show that this ratio is tight.
- M. Ajtai, J. Aspnes, C. Dwork, and O. Waarts. A theory of competitive analysis for distributed algorithms. In Proceedings of the 35th Symposium on Foundations of Computer Science (FOCS 1994), pages 401--411, 1994.]]Google ScholarDigital Library
- B. Awerbuch, S. Kutten, and D. Peleg. Competitive distributed job scheduling. In Proceedings of the 24th ACM Symposium on Theory of Computing (STOC 1992), pages 571--580, 1992.]] Google ScholarDigital Library
- O. Babaoglu, R. Davoli, A. Montresor, and R. Segala. System support for partition-aware network applications. In Proceedings of the 18th IEEE International Conference on Distributed Computing Systems (ICDCS 1998), pages 184--191, 1998.]] Google ScholarDigital Library
- Y. Bartal, A. Fiat, and Y. Rabani. Competitive algorithms for distributed data management. In Proceedings of the 24th ACM Symposium on Theory of Computing (STOC 1992), pages 39--50, 1992.]] Google ScholarDigital Library
- S. Ben-David, A. Borodin, R. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11(1):2--14, 1994.]]Google ScholarDigital Library
- B. Chlebus, R. De Prisco, and A.A. Shvartsman. Performing tasks on restartable message passing processors. Distributed Computing, 14(1):49--64, 2001.]] Google ScholarDigital Library
- R. De Prisco, A. Mayer, and M. Yung. Time-optimal message-efficient work performance in the presence of faults. In Proceedings of the 13th ACM Symposium on Principles of Distributed Computing (PODC 1994), pages 161--172, 1994.]] Google ScholarDigital Library
- R.P. Dilworth. A decomposition theorem for partially ordered sets. Annals of Mathematics, 51:161--166, 1950.]]Google ScholarCross Ref
- S. Dolev, R. Segala, and A.A. Shvartsman. Dynamic load balancing with group communication. In Proceedings of the 6th International Colloquium on Structural Information and Communication Complexity (SIROCCO 1999), pages 111--125, 1999.]]Google Scholar
- C. Dwork, J. Halpern, and O. Waarts. Performing work efficiently in the presence of faults. SIAM Journal on Computing, 27(5):1457--1491, 1998. A preliminary version appears as "Accomplishing work in the presence of failures" in the Proceedings of the 11th ACM Symposium on Principles of Distributed Computing (PODC 1992), pages 91--102, 1992.]] Google ScholarDigital Library
- A. Fiat, R.M. Karp, M. Luby, L.A. McGeoch, D.D. Sleator, and N.E. Young. Competitive paging algorithms. Journal of Algorithms, 12(4):685--699, 1991.]] Google ScholarDigital Library
- S. Georgiades, M. Mavronicolas, and P. Spirakis. Optimal, distributed decision-making: The case of no communication. In Proceedings of the 12th Int-l Symposium on Foundamentals of Computation Theory (FCT 1999), pages 293--303, 1999.]] Google ScholarDigital Library
- Ch. Georgiou, A. Russell, and A.A. Shvartsman. Optimally work-competitive scheduling for cooperative computing with merging groups (brief announcement). In Proceedings of the 22nd ACM Symposium on Principles of Distributed Computing (PODC 2002), 2002.]] Google ScholarDigital Library
- Ch. Georgiou and A.A. Shvartsman. Cooperative computing with fragmentable and mergeable groups. Journal of Discrete Algorithms, to appear. (Also in Proc. of the 7th Int-l Colloquium on Structural Information and Communication Complexity (SIROCCO 2000), pages 141--156, 2000).]] Google ScholarDigital Library
- P.C. Kanellakis and A.A. Shvartsman. Fault-Tolerant Parallel Computation. Kluwer Academic Publishers, 1997.]] Google ScholarDigital Library
- G.G. Malewicz, A. Russell, and A. A. Shvartsman. Distributed cooperation during the absence of communication. In Proceedings of the 14th International Symposium on Distributed Computing (DISC 2000), pages 119--133, 2000.]] Google ScholarDigital Library
- C.H. Papadimitriou and M. Yannakakis. On the value of information in distributed decision making. In Proceedings of the 10th ACM Symposium on Principles of Distributed Computing (PODC 1991), pages 61--64, 1991.]] Google ScholarDigital Library
- D. Powell, editor. Special Issue on Group Communication Services, volume 39(4) of Communications of the ACM. ACM Press, 1996.]] Google ScholarDigital Library
- M. Saks, N. Shavit, and H. Woll. Optimal time randomized consensus -- making resilient algorithms fast in practice. In Proceedings of the 2nd ACM-SIAM Symposium on Discrete Algorithms (SODA 1991), pages 351--362, 1991.]] Google ScholarDigital Library
- D. Sleator and R. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28(2):202--208, 1985.]] Google ScholarDigital Library
- J.B. Sussman and K. Marzullo. The bancomat problem: An example of resource allocation in a partitionable asynchronous system. In Proceedings of the 12th International Symposium on Distributed Computing (DISC 1998), pages 363--377, 1998.]] Google ScholarDigital Library
Index Terms
- Work-competitive scheduling for cooperative computing with dynamic groups
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