Byzantine gathering in polynomial time

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 study of gathering an arbitrary graph: despite presence agents, goal ensure that all other (good) executing same algorithm, eventually meet at node stop. Initially, each agent gets input different label global knowledge common agents. The move synchronous rounds communicate with only when located node. There f These act unpredictable way, e.g., they may convey informations or forge any label. In literature, algorithms working such context have exponential time complexity number n nodes labels good this paper, we design deterministic algorithm solve polynomial logarithm $$\ell $$ smallest agent, provided strong team i.e., where least quadratic f. Our requires can be coded $$O(\log \log n)$$ bits: prove size optimal order magnitude obtain teams.