An inherent bottleneck in distributed counting
Roger P. Wattenhofer, Peter Widmayer · 1997
A distributed counter allows each processor in an asynchronous message passing network to access the counter value and increment it We study the problem of implementing a distributed counter such that no processor is a communication bottleneck We prove a lower bound of k on the number of messages that some processor must exchange in a sequence of n counting operations spread over n processors where kkk n We propose a counter that achieves this bound for the situation it is derived for namely when each processor increments the counter exactly once Hence the lower bound is tight Because most algorithms and data structures count in some way the lower bound holds for many distributed computations We feel that the proposed concept of a communication bottleneck is a relevant measure of eciency for a distributed algorithm and data structure because it indicates the achievable degree of distribution.