Robustness and Failure Detection in Epistemic Gossip Protocols

Abstract

Gossip problem is an information dissemination problem in which networked agents (nodes) must share their secrets by the minimum number of calls. In recent years, to solve the problem, various epistemic gossip protocols have been proposed, where the agents decide who to call based on the higher-order knowledge about the possession of secrets. Although most previous studies on the epistemic gossip protocol have restricted their scope to the environments including only reliable agents, from the practical viewpoint, it is worthwhile investigating robust protocols against agent failure. In this paper, we assume the existence of unreliable agents and analyze the robustness of some existing protocols using epistemic logic. In our model, when an agent fails, it loses the secrets and telephone numbers gained by previous calls and returns to its initial state. In addition, during each call, agents share not only their possessing secrets but also the history of the transmission path of each secret. For these settings, we show that the protocols ANY and PIG are successful (i.e., the protocols always lead to the state where every agent knows all secrets). We also show that the protocol CO is not immediately successful under the assumption that agents can fail, but it becomes successful if the protocol execution satisfies some conditions. Furthermore, we clarify sufficient conditions for agents to detect the failure of other agent, which are useful for designing robust protocols.