1 research outputs found
The string of diamonds is nearly tight for rumour spreading
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
-vertex graph and any starting vertex, the ratio between their expected
spread times is bounded by . This
improves the 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 , as illustrated by the string of
diamonds graph. We also show that if for a pair of real numbers,
there exists infinitely many graphs for which the two spread times are
and in expectation, then and
; and we show each such pair
is achievable.Comment: Will be presented at RANDOM'2017 conference. 14 pages, Theorem 2.5
added in this versio