Journal of the Association for Computing Machinery, Vol. 42, No. 2, March 1995, pp. 382–400.

On the Average Communication Complexity of Asynchronous Distributed Algorithms

JOHN N. TSITSIKLIS

AND

GEORGE D. STAMOULIS

Abstract. We study the communication complexity of asynchronous distributed algorithms. Such algorithms can generate excessively many messages in the worst case. Nevertheless, we show that, under certain probabilistic assumptions, the expected number of messages generated per time unit is bounded by a polynomial function of the number of processors under a very general model of distributed computation. Furthermore, for constant-degree processor graphs, the expected number of generated messages is only O(nT), where n is the number of processors and T is the running time. We conclude that (under our model) any asynchronous algorithm with good time complexity will also have good communication complexity, on the average.

Categories and Subject Descriptors. C.2.1[network communication]; G.1.0[parallel algorithms]; G.m[Queueing theory]]

General Terms. Algorithms, performance

Additional Key words and Phrases. asynchronous distributed algorithms

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