Paper 2013/533

Gossip Latin Square and The Meet-All Gossipers Problem

Nethanel Gelernter and Amir Herzberg

Abstract

Given a network of n = 2^k gossipers, we want to schedule a cyclic calendar of meetings between all of them, such that: (1) each gossiper communicates (gossips) only once a day, with one other gossiper, (2) in every (n 1) consecutive days, each gossiper meets all other gossipers, and (3) every gossip, initiated by any gossiper, will reach all gossipers within k = log(n) days. In this paper we study the above stated meet-all gossipers problem, by den-ing and constructing the Gossip Latin Square (GLS), a combinatorial structure which solves the problem.