Dynamic Gossip

TL;DR

This paper studies distributed dynamic gossip protocols where agents exchange secrets and identities, characterizing success conditions based on graph connectivity, and revealing surprising differences between protocols.

Contribution

It introduces six distributed dynamic gossip protocols and characterizes their success conditions in terms of graph connectivity, including novel results for a protocol with restricted calling rules.

Findings

Strong success is characterized by weak connectivity for five protocols.

The sixth protocol's success depends on strong connectivity of non-terminal nodes.

Certain success conditions are surprisingly complex to prove.

Abstract

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. The goal is for all agents to get to know all secrets, in which case we call the execution of the protocol successful. We consider distributed and dynamic gossip protocols. In distributed gossip the agents themselves instead of a global scheduler determine whom to call. In dynamic gossip not only secrets are exchanged but also telephone numbers (agent identities). This results in increased graph connectivity. We define six such distributed dynamic gossip protocols, and we characterize them in terms of the topology of the graphs on which they are successful, wherein we distinguish strong success (the protocol always terminates, possibly assuming fair scheduling) from weak success (the protocol sometimes terminates). For five of these protocols strong (fair) and weak success are characterized by weakly connected graphs. This result is surprising because the protocols are fairly different. In the sixth protocol an agent may only call another agent if it does not know the other agent's secret. Strong success for this protocol is characterized by graphs for which the set of non-terminal nodes is strongly connected. Weak success for this protocol is characterized by weakly connected graphs satisfying further topological constraints that we define in the paper. One direction of this characterization is surprisingly harder to prove than the other results in this contribution.