The string of diamonds is nearly tight for rumour spreading

Omer Angel, Abbas Mehrabian, Yuval Peres

Abstract: For a rumour spreading protocol, the spread time is defined as the first time everyone learns the rumour. We compare the synchronous push&pull rumour spreading protocol with its asynchronous variant, and show that for any n-vertex graph and any starting vertex, the ratio between their expected spread times is bounded by ; and we show each such pair α, β is achievable.