Gossiping without Duplicate Transmissions
Douglas B. West · SIAM Journal on Algebraic and Discrete Methods · 1982
n people have distinct bits of information, which they communicate via telephone calls in which they transmit everything they know. We require that no one ever hear the same piece of information twice. In the case 4 divides $n,\,n\geqq 8$, we provide a construction that transmits all information using only $9n/4 - 6$ calls. Previous constructions used $\frac{1}{2}n \log n$ calls.