Brief Announcement: Gathering Despite a Linear Number of Weakly Byzantine Agents

We study the gathering problem to make multiple agents initially scattered in arbitrary networks gather at a single node. There exist k agents with unique identifiers (IDs) in the network, and.. of them are weakly Byzantine agents, which behave arbitrarily except for falsifying their IDs. The agents behave in synchronous rounds, and each node does not have any memory like a whiteboard. In the literature, there exists a gathering algorithm that tolerates any number of Byzantine agents, while the fastest gathering algorithm requires Omega(f(2)) non-Byzantine agents. This paper proposes an algorithm that solves the gathering problem efficiently with Omega(f(2)) non-Byzantine agents since there is a large gap between the number of non-Byzantine agents in the previous works. The proposed algorithm achieves the gathering in O(f center dot |Lambda(good) | center dot X (Nu)) rounds in case of 9f + 8 <= k and simultaneous startup if.. is given to agents, where ||Lambda(good) | | is the length of the largest ID among nonByzantine agents, and |Lambda(good) | is the number of rounds required to explore any network composed of n nodes. This algorithm is faster than the most fault-tolerant existing algorithm and requires fewer non-Byzantine agents than the fastest algorithm if.. is given to agents, although the guarantees on simultaneous termination and startup delay are not the same. To achieve this property, we propose a new technique to simulate a Byzantine consensus algorithm for synchronous message-passing systems on agent systems.