On Optimal Solutions to the Problem of Gossiping in Minimum Time

We determine solutions to the problem of gossiping in minimum time (briefly: minimum time problem or MTP) which require less calls than the previously known solutions for infinitely many values of the number \(n\) of persons and optimal solutions to the MTP, i.e. solutions of the MTP which minimize the number of calls, for some values of \(n\). We conjecture that our methods provide optimal solutions of the MTP for all \(n\).