An O(n log n) Unidirectional Distributed Algorithm for Extrema Finding in a Circle

In this paper we present algorithms, which given a circular arrangement of n uniquely numbered processes, determine the maximum number in a distributive manner . We begin with a simple unidirectional algorithm, in which the number of messages passed is bounded by 2n log n + 0(n) . By making several improvements to the simple algorithm, we obtain a unidirectional algorithm in which the number of messages passed is bounded by 1 .5n logn + 0(n) . These algorithms disprove Hirschberg and Sinclair's'conjecture that 0(n 2 ) is a lower bound on the number of messages passed in undirectional algorithms for this problem . At the end of the paper we indicate how our methods can be used to improve an algorithm due to Peterson, to obtain a unidirectional algorithm using at most 1 .356n log n + 0(n) messages. This is the best bound so far on the number of messages passed in both the bidirectional and unidirectional cases .