The renowned Gossiping Problem (1971) asks the following. There are n people who each know an item of gossip. In a telephone call, two people share all the gossip they know. How many calls are needed for all of them to be informed of all the gossip? If n≥4, the answer is 2n−4. We initiate and solve the related Greedy Gossiping Problem: given a fixed number m<2n−4 of calls, at most how much gossip can be known altogether? If every call increases the total knowledge of gossip as much as possible, the sum reaches n2 only when m=2n−3. Our main result is that surprisingly, for each m<2n−4, this calling strategy is optimal.
Cite
@article{arxiv.2506.17804,
title = {Greedy Gossiping},
author = {Kada Williams},
journal= {arXiv preprint arXiv:2506.17804},
year = {2025}
}