On Fast and Robust Information Spreading in the Vertex-Congest Model

TL;DR

This paper studies how failures affect information spreading in the Vertex-Congest model, showing that adaptive algorithms significantly improve speed over naive methods despite failures.

Contribution

It introduces a dynamic probability-based algorithm for information spreading that is robust and faster than uniform random forwarding under failures.

Findings

Randomized uniform forwarding is slow on certain graphs.

Adaptive algorithms achieve near-optimal spreading times.

The proposed method handles failures effectively.

Abstract

This paper initiates the study of the impact of failures on the fundamental problem of \emph{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. 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 $\Omega(n/\sqrt{k})$ 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 $O(n\log^3{n}/k)$ rounds, despite a rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing probabilities that change according to the execution is of independent interest.