Tentative and definite distributed computations: An optimistic approach to network synchronization
We present here a general and efficient strategy for simulating a synchronous network by a network of limited asynchrony. Our proposed synchronizer is optimistic in the sense that it uses very efficient but tentative protocols to simulate a contiguous block of synchronous steps. However, since a tentative execution does not guarantee correct simulation, we audit the computation at selected points. The audits are used to check whether the computation of the block can be certified to be correct. We show that a wide class of networks of limited asynchrony admits practical tentative protocols which are highly likely to produce a correct simulation of one step with very small overhead. For those networks, the synchronizer exhibits a trade-off between its communication and time complexities which is below the lower bounds for deterministic synchronizers. On one extreme the amortized complexity of our synchronizer is O(1) messages and O(log n) time (expected) per “step” of the simulated synchronous protocol. On the other extreme the communication complexity is O(e/Δ2) and the time complexity is O(logΔ), for networks with e edges and maximum degree Δ.
Unable to display preview. Download preview PDF.
- [A,85]Awerbuch B., “Complexity of Network Synchronization”, JACM, Vol. 32, No 4, Oct. 1985.Google Scholar
- [AP,90]Awerbuch B., Peleg D., “Network Synchronization with Polylogarithmic Overhead”, Proc. IEEE FOCS, 1990.Google Scholar
- [CHEP,71]C Commoner F., Holt W., Even S., Pnueli A., “Marked Directed Graphs”, JCSS, Vol. 5, No 5, 1971.Google Scholar
- [CL,85]Chandy K.M., Lamport L., “Distributed Snapshots: Determining Global States of Distributed Systems”, ACM Trans. on Computer Systems, Vol. 3, No 1, 1985.Google Scholar
- [ER,88]Even E., Rajsbaum S., “Lack of Global Clock Does Not Slow Down the Computation in Distributed Networks”, TR #522, Dep. of Comp. Sc., Haifa, Israel, Oct. 1988. The first part of this paper will appear with the title “Unison in Distributed Networks” in Sequenses, Combinatorica, Compression, Security and Transmission, R.M. Capocelli (ed.), Springer-Verlag.Google Scholar
- [ER,90]Even E., Rajsbaum S., “The use of a Synchronizer Yields Maximum Rate in Distributed Networks”, Proc. 22nd ACM STOC, 1990.Google Scholar
- [KPRS,91]Kedem Z., Palem K., Raghunathan A., Spirakis P., “Combining Tentative and Definite Executions for Very Fast Dependable Parallel Computing”, Proc. ACM STOC 1991.Google Scholar
- [PU,89]Peleg D., Ullman J., “An Optimal Synchronizer for the Hypercube”, SIAM J.Computing, Vol. 18, No 4, Aug. 1989, pp 740–747.Google Scholar
- [Ro,83]Ross S.M., “Stochastic Processes”, Wiley, 1983.Google Scholar
- [RS,90]Rajsbaum S., Sidi M., “On the Average Performance of Synchronized Programs in Distributed Networks”, Proc. WDAG 1990.Google Scholar
- [Wy,81]J. C. Wyllie, “The Complexity of Parallel Computations”, PhD dissertation, Comp. Sc. Department, Cornell University, Ithaca, New York, 1981.Google Scholar