Asynchronous Rumor Spreading on Random Graphs

Abstract

We perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erdős-Rényi 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 pushpull protocol is asymptotically almost unaffected by the average degree of the graph. Similarly tight bounds for Erdős-Rényi 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.

Asymptotics for Pull on the Complete Graph

“…In [17] it was shown that, after appropriate normalization, the limiting distribution of the runtime of asynchronous pull on complete graphs converges and the limit is the sum of two independent Gumbel distributed random variables. Some more recent results on asynchronous rumor spreading are [15,19,22].…”