Deterministic leader election in O(D + log n) time with messages of size O(1)

Abstract

This paper presents a distributed algorithm, called STT, for electing deterministically a leader in an arbitrary network, assuming processors have unique identifiers of size O(log n), where n is the number of processors. It elects a leader in O(D + logn) rounds, where D is the diameter of the network, with messages of size O(1). Thus it has a bit round complexity of O(D+log n). This substantially improves upon the best known algorithm whose bit round complexity is O(Dlog n). In fact, using the lower bound by Kutten et al. [13] and a result of Dinitz and Solomon [8], we show that the bit round complexity of ST T is optimal (up to a constant factor), which is a step forward in understanding the interplay between time and message optimality for the election problem. Our algorithm requires no knowledge on the graph such as n or D.