Deterministic Leader Election Takes Θ (D + log n) Bit Rounds

Leader election is, together with consensus, one of the most central problems in distributed computing. 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 +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. (J ACM 62(1):7:1–7:27, 2015 ) and Kutten et al. (Theor Comput Sci 561:134–143, 2015 ) and a result of Dinitz and Solomon (Theor Comput Sci 384(2–3):168–183, 2007 ), we show that the bit round complexity of 𝒮𝒯𝒯 is optimal (up to a constant factor), which is a significant 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 , and the pipelining technique we introduce to break the O(Dlog n) barrier is general.