Rules for Optimal Perpetual Gossiping Schemes

Perpetual gossiping is an all-to-all communication problem on social networks, or any coordinated distributed system in general. In perpetual gossiping, a state of universal reachability is maintained by a continuous sequence of communications between participants. Unlike the well-understood static case, perpetual gossiping is a difficult problem, with some NP-complete classes of solutions. A basic question which remains open is whether an optimal scheme of contiguous calls is guaranteed to exist for a tree. This paper presents a series of theoretical tools directed towards answering the question.