Weakly Byzantine Gathering with a Strong Team

We study the gathering problem requiring a team of mobile agents to gather at single node in arbitrary networks. The consists k with unique identifiers (IDs), and f them are weakly Byzantine agents, which behave arbitrarily except falsifying their identifiers. move synchronous rounds cannot leave any information on nodes. If number nodes n is given existing fastest algorithm tolerates achieves simultaneous termination O(n4·|Λgood|·X(n)) rounds, where |Λgood| length maximum ID non-Byzantine X(n) required explore network composed In this paper, we ask question whether can reduce time complexity if have strong team, i.e., few because not so many subject faults practice. give positive answer by proposing two algorithms case least 4f2+9f+4 exist. Both assume that upper bound N agents. first non-simultaneous O((f+|Λgood|)·X(N)) rounds. second O((f+|Λall|)·X(N)) |Λall| all significantly reduces compared one |Λall|=O(|Λgood|) holds.