Robust gossiping with an application to consensus

We study deterministic gossiping in synchronous systems with dynamic crash failures. Each processor is initialized with an input value called rumor. In the standard gossip problem, the goal of every processor is to learn all the rumors. When processors may crash, then this goal needs to be revised, since it is possible, at a point in an execution, that certain rumors are known only to processors that have already crashed. We define gossiping to be completed, for a system with crashes, when every processor knows either the rumor of processor v or that v has already crashed, for any processor v. We design gossiping algorithms that are efficient with respect to both time and communication. Let t