Gathering with a strong team in weakly Byzantine environments
Jion Hirose, Junya Nakamura, Fukuhito Ooshita, Michiko Inoue

TL;DR
This paper improves gathering algorithms for mobile agents in networks by reducing time complexity when the team has fewer Byzantine agents, using new algorithms that leverage the number of agents and ID lengths.
Contribution
It introduces two new algorithms for gathering with fewer Byzantine agents, achieving faster convergence and simultaneous termination under certain conditions.
Findings
First algorithm achieves non-simultaneous gathering in O((f+|Λ_good|)·X(N)) rounds.
Second algorithm achieves simultaneous gathering in O((f+|Λ_all|)·X(N)) rounds.
Significant reduction in time complexity when |Λ_all|=O(|Λ_good|) and n is known.
Abstract
We study the gathering problem requiring a team of mobile agents to gather at a single node in arbitrary networks. The team consists of agents with unique identifiers (IDs), and of them are weakly Byzantine agents, which behave arbitrarily except falsifying their identifiers. The agents move in synchronous rounds and cannot leave any information on nodes. If the number of nodes is given to agents, the existing fastest algorithm tolerates any number of weakly Byzantine agents and achieves gathering with simultaneous termination in rounds, where is the length of the maximum ID of non-Byzantine agents and is the number of rounds required to explore any network composed of nodes. In this paper, we ask the question of whether we can reduce the time complexity if we have a strong team, i.e., a team with a few…
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Taxonomy
TopicsOptimization and Search Problems · Distributed systems and fault tolerance · Auction Theory and Applications
