Synchronous T-Resilient Consensus In Arbitrary Graphs

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 that considers all ways in which t nodes may crash, and present an algorithm that solves consensus in radius rounds. Then we derive a lower bound showing that our algorithm is optimal for vertex-transitive graphs, among oblivious algorithms.