Synchronous t-Resilient Consensus in Arbitrary Graphs

16^th October 2021, 00:00
Armando Castaneda
Universidad Nacional Autonoma de Mexico

Abstract

We study the number of rounds needed to solve consensus in a synchronous network G where at most t nodes may fail by crashing. This problem has been thoroughly studied when G is a complete graph, but very little is known when G is arbitrary. We define a notion of radius(G, t), that extends the standard graph theoretical notion of radius, for considering all the ways in which t nodes may crash, and we present an algorithm that solves consensus in radius(G, t) rounds. Then we derive a lower bound showing that, among oblivious algorithms, our algorithm is optimal for a large family of graphs including all vertex-transitive graphs.

This is a joint work with Pierre Fraigniaud, Ami Paz, Sergio Rajsbaum, Matthieu Roy and Corentin Travers.