A SIMPLE, EFFICIENT ALGORITHM FOR MAXIMUM FINDING ON RINGS

The maximum finding problem is: given a network of processors with distinct identifiers, find that processor with the maximum identifier. We present a new deterministic algorithm for maximum finding on asynchronous unidirectional rings. For the past decade, the record for the lowest worst case message complexity (1.356n log n + O(n)) for maximum finding for this model has been held by an involved algorithm with a complicated analysis. Our algorithm is simple, has a very much simpler analysis and achieves a lower worst case message complexity (less than 1.271n log n + O(n) messages). An additional contribution of this paper is a new perspective on this problem that exhibits its structure thus permitting a better understanding of various message saving mechanisms.