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

Arnaud Casteigts (1) , Yves Métivier (1) , John Michael M Robson (1) , Akka Zemmari (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Leader election is, together with consensus, one of the most central problems in distributed computing. This paper presents a distributed algorithm, called ST T , 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. (2015) and a result of Dinitz and Solomon (2007), we show that the bit round complexity of ST T 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.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Réseaux et télécommunications [cs.NI]

Arnaud Casteigts, Yves Métivier, John Michael M Robson, Akka Zemmari. Deterministic Leader Election Takes Θ(D + log n) Bit Rounds. Algorithmica, 2019, 81 (5), pp.1901-1920. ⟨10.1007/s00453-018-0517-3⟩. ⟨hal-01883355⟩