Optimal Fast Solutions to the Gossip Problem

We present a new proof that the optimal fast solutions to the gossip problem, for an even number of participants \( n > 2^{\lceil \log_2{n} \rceil} – 2^{\lfloor \lceil \log_2{n} \rceil /2\rfloor} \), require exactly \( \frac{n}{2}\lceil \log_2{n} \rceil \) calls.