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

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

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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. [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.

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

Arnaud Casteigts, Yves Métivier, John Michael Robson, Akka Zemmari. Deterministic Leader Election in $O(D+\log n)$ Time with Messages of Size $O(1)$. 30th International Symposium on Distributed Computing (DISC), Sep 2016, Paris, France. pp.16-28, ⟨10.1007/978-3-662-53426-7_2⟩. ⟨hal-01472671⟩