Gathering is a key task in distributed and mobile systems, which becomes significantly harder if some agents are subject to Byzantine faults, known as being the worst ones. We propose here to study the task of Byzantine gathering in an arbitrary graph: despite the presence of Byzantine agents, the goal is to ensure that all the other (good) agents, executing the same algorithm, eventually meet at the same node and stop. Initially, each agent gets as input a different label and some global knowledge that is common to all agents. The agents move in synchronous rounds and communicate with each other only when located at the same node. There are f Byzantine agents. These agents act in an unpredictable way, e.g., they may convey arbitrary informations or forge any label. In the literature, the gathering algorithms working in such a context all have an exponential time complexity in the number n of nodes and the labels of the good agents. In this paper, we design a deterministic algorithm to solve Byzantine gathering in time polynomial in n and the logarithm \(\ell \) of the smallest label of a good agent, provided the agents are a strong team i.e., a team where the number of good agents is at least some quadratic polynomial in f. Our algorithm requires global knowledge that can be coded in \(O(\log \log \log n)\) bits: we prove this size is of optimal order of magnitude to obtain a polynomial time complexity in n and \(\ell \) with strong teams.

收集是分布式和移动系统中的一项关键任务，如果某些代理受到拜占庭错误的影响，这将变得更加困难，被称为最糟糕的错误。我们在这里建议研究拜占庭在任意图中收集的任务：尽管存在拜占庭代理，但目标是确保执行相同算法的所有其他（好的）代理最终在同一节点相遇并停止。最初，每个代理都获得一个不同的标签和一些所有代理共有的全局知识作为输入。代理在同步轮次中移动，并且仅当位于同一节点时才相互通信。有f拜占庭特工。这些代理以不可预知的方式行事，例如，它们可能传达任意信息或伪造任何标签。在文献中，在这种情况下工作的收集算法在节点数n和好代理的标签上都具有指数时间复杂度。在本文中，我们设计了一种确定性算法来解决n中的拜占庭时间多项式和一个好的代理的最小标签的对数\(\ell\)，假设代理是一个强大的团队，即一个团队的数量好的代理至少是f中的一些二次多项式。我们的算法需要可以编码为\(O(\log \log \log n)\)的全局知识位：我们证明这个大小是最佳数量级，可以在n和\(\ell \)中获得多项式时间复杂度，并拥有强大的团队。