Gathering of Anonymous Agents

Motivated by the increasing popularity of mobile agents and swarm robotics, we study the fundamental and widely studied problem of gathering 𝑘 autonomous and anonymous agents placed in arbitrary vertices of a graph comprising 𝑛 nodes. In this work, we present algorithms that, for the first time, ensure gathering of anonymous mobile agents in any arbitrary graph. Moreover, our algorithms are fast. The canonical case where the graph is complete and 𝑘 = 𝑛 runs in expected time that is sublogarithmic in 𝑛. Importantly, these robot swarms are often deployed in vulnerable contexts where security may be compromised. Thus, we consider the case where 𝑓 of the agents are Byzantine (i.e., compromised and therefore malicious) and can deviate from the protocol in an adversarial manner. Our main result is a fast gathering algorithm when the Byzantine agents are controlled by a strongly adaptive adversary that-in each round-can view all the moves made by the good agents and then strategically make the moves of all Byzantine agents in a coordinated fashion. For the canonical case where the graph is complete and 𝑘 = 𝑛, we provide a gathering algorithm that runs in time that is polylogarithmic in 𝑛 provided 𝑓 ∈ O (𝑘/log 𝑘). This is the first known result on gathering anonymous agents with Byzantine failures. Our results generalize to arbitrary graphs and hold with high probability. Moreover, we complement our upper bounds with lower bounds that are tight to within polylog(𝑛) factors.