Rumor Spreading on Percolation Graphs

TL;DR

This paper analyzes how rumor spreading efficiency in a regular graph is affected by percolation, showing that the rumor propagates nearly as fast in the percolated graph as in the original, under certain conditions.

Contribution

It establishes a relationship between rumor spreading times in regular graphs and their percolated counterparts, providing bounds on the spreading time after percolation.

Findings

Rumor spreads within T rounds in G imply similar speed in G_p.

Spreading time in G_p is at most (1 + ε) times T under specified conditions.

The results hold when T = o(pd), linking graph degree, percolation probability, and spreading efficiency.

Abstract

We study the relation between the performance of the randomized rumor spreading (push model) in a d-regular graph G and the performance of the same algorithm in the percolated graph G_p. We show that if the push model successfully broadcast the rumor within T rounds in the graph G then only (1 + \epsilon)T rounds are needed to spread the rumor in the graph G_p when T = o(pd).