Deterministic Leader Election in O(D+\log n) Time with Messages of Size O(1).

This paper presents a distributed algorithm, called (mathcal{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 +log n)) 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 (mathcal{STT}) 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.