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- W3100777130 abstract "For a rumour spreading protocol, the spread time is defined as the first time that 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 $O left({n}^{1/3}{log^{2/3} n}right)$. This improves the $O(sqrt n)$ upper bound of Giakkoupis, Nazari, and Woelfel (in Proceedings of ACM Symposium on Principles of Distributed Computing, 2016). Our bound is tight up to a factor of $O(log n)$, as illustrated by the string of diamonds graph. We also show that if for a pair $alpha,beta$ of real numbers, there exists infinitely many graphs for which the two spread times are $n^{alpha}$ and $n^{beta}$ in expectation, then $0leqalpha leq 1$ and $alpha leq beta leq frac13 + frac23 alpha$; and we show each such pair $alpha,beta$ is achievable." @default.
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- W3100777130 date "2019-11-04" @default.
- W3100777130 modified "2023-10-14" @default.
- W3100777130 title "The string of diamonds is nearly tight for rumour spreading" @default.
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- W3100777130 doi "https://doi.org/10.1017/s0963548319000385" @default.
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