Asynchronous Rumor Spreading on Random Graphs

TL;DR

This paper analyzes the asynchronous push-pull rumor spreading protocol on Erdős-Rényi random graphs, showing it spreads information efficiently with tight bounds on time, unaffected by graph sparsity, and demonstrates robustness against failures.

Contribution

It introduces a simple analysis strategy for asynchronous rumor spreading on arbitrary graphs and provides tight bounds for Erdős-Rényi graphs, highlighting robustness and efficiency.

Findings

Total spreading time is logarithmic and unaffected by average degree.

Asynchronous protocol is robust to transmission and node failures.

Results extend understanding of rumor spreading dynamics on random graphs.

Abstract

We perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erd\H{o}s-R\'enyi random graphs $G_{n,p}$, for any $p>c\ln(n)/n$ with $c>1$. In particular, we provide a simple strategy for analyzing the asynchronous push-pull protocol on arbitrary graph topologies and apply this strategy to $G_{n,p}$. We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous push-pull protocol is asymptotically almost unaffected by the average degree of the graph. Similarly tight bounds for Erd\H{o}s-R\'enyi random graphs have previously only been obtained for the synchronous push protocol, where it has been observed that the total running time increases significantly for sparse random graphs. Finally, we quantify the robustness of the protocol with respect to transmission and node failures. Our analysis suggests that the asynchronous protocols are particularly robust with respect to these failures compared to their synchronous counterparts.