Spreading rumors rapidly despite an adversary

Abstract

In the collect problem (M. Saks, N. Shavit, and H. Woll, in "Proceedings of the 2nd ACM-SIAM Symposium on Discrete Algorithms, 1991), n processors in a shared-memory system must each learn the values of n registers We give a randomized algorithm that solvesthe collect problem in O(n log3 n) total read and write operations with high probability, even if timing is under the control of a content-oblivious adversary (a slight weakening of the usual adaptive adversary). This improves on both the trivial upper bound of O(n2) steps and the best previously known bound of O(n3/2 log n) steps, and is dose to the lower bound of Ω(n log n) steps Furthermore, we show how this algorithm can be used to obtain a multiuse cooperative collect protocol that is O(log3 n)-competitive in the latency model of Ajtai et al. ("Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science," 1994); and O(n1/2 log3/2 n)-competitive in the throughput model of Aspnes and Waarts ("Proceedings of the 28th ACM Symposium on Theory of Computing," 1996). In both cases the competitive ratios are within a polylogarithmic factor of optimal, © 1998 Academic Press.