Fast gathering despite a linear number of weakly Byzantine agents†

Abstract

SummaryIn this work, we study the gathering problem to make multiple agents, who are initially scattered in arbitrary networks, meet at the same node. The network has agents with unique identifiers (IDs), and of them are weakly Byzantine agents that behave arbitrarily, except for falsifying their identifiers. These agents behave in synchronous rounds, and they may start an algorithm at different rounds. Each agent cannot leave information at a node. We propose herein a deterministic algorithm that efficiently achieves gathering with a simultaneous termination having a small number of non‐Byzantine agents. The proposed algorithm concretely works in rounds if the agents know the upper bound on the number of nodes, and at least non‐Byzantine agents exist, where is the length of the largest ID among agents, and is the number of rounds required to explore any network composed of nodes. The literature presents two efficient gathering algorithms with a simultaneous termination. The first algorithm assumes that agents know the number of nodes and achieves the gathering in rounds in the presence of any number of Byzantine agents, where is the length of the largest ID among non‐Byzantine agents. The second algorithm assumes both that agents know and that at least non‐Byzantine agents exist, and it achieves the gathering in rounds. The proposed algorithm is faster than the first existing algorithm and requires fewer non‐Byzantine agents than the second existing algorithm if is given to agents. We propose herein a new technique to simulate a Byzantine consensus algorithm for synchronous message‐passing systems on agent systems to reduce the number of agents.