Gathering despite a linear number of weakly Byzantine agents
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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 f 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 Ω(f^2) non-Byzantine agents. This paper proposes an algorithm that solves the gathering problem efficiently with Ω(f) non-Byzantine agents since there is a large gap between the number of non-Byzantine agents in previous works. The proposed algorithm achieves the gathering in O(f·|Λ_good|· X(N)) rounds in case of 9f+8≤ k and simultaneous startup if N is given to agents, where |Λ_good| is the length of the largest ID among non-Byzantine agents, and X(n) 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 n 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.
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