On fast and robust information spreading in the Vertex-Congest model

This paper initiates the study of the impact of failures on the fundamental problem of information spreading in the Vertex-Congest model, in which in every round, each of the n nodes sends the same O(log⁡n)-bit message to all of its neighbors. We consider a strong failure model, in which links are reliable but nodes fail independently with probability q per round and never recover. Our contribution to coping with failures is twofold. First, we prove that the randomized algorithm which chooses uniformly at random the next message to forward is slow, requiring Ω(n/k) rounds on some graphs, which we denote by G_n,k, where k is the vertex-connectivity. Second, we design a randomized algorithm that makes dynamic message choices, with probabilities that change over the execution. We prove that for G_n,k it requires only a near-optimal number of O(nlog³⁡n/k) rounds, despite a rate of q=O(k/nlog³⁡n) failures per round. Our technique of choosing probabilities that change according to the execution is of independent interest.