Deterministic Leader Election Takes Θ(D+logn) 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 ( D log 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 ( D log n ) barrier is general.