Gossip Latin Square And The Meet-All Gossipers Problem

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 meets (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 defining and constructing the Gossip Latin Square (GLS), a combinatorial structure which solves the problem. We then present an efficient construction of GLS, based on maximal Fibonacci LFSR. (C) 2015 Elsevier B.V. All rights reserved.