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Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents

Authors Jion Hirose , Ryota Eguchi , Yuichi Sudo

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed algorithms
  • Byzantine environments
  • Gathering

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Abstract

We study the Byzantine gathering problem involving k mobile agents with unique identifiers (IDs), f of which are Byzantine. These agents start the execution of a common algorithm from (possibly different) nodes in an n-node network, potentially starting at different times. Once started, the agents operate in synchronous rounds. We focus on weakly Byzantine environments, where Byzantine agents can behave arbitrarily but cannot falsify their IDs. The goal is for all non-Byzantine agents to eventually terminate at a single node simultaneously.
In this paper, we first prove two impossibility results: (1) for any number of non-Byzantine agents, no algorithm can solve this problem without global knowledge of the network size or the number of agents, and (2) no self-stabilizing algorithm exists if k ≤ 2f even with n, k, f, and the length Λ_g of the largest ID among IDs of non-Byzantine agents, where the self-stabilizing algorithm enables agents to gather starting from arbitrary (inconsistent) initial states. Next, based on these results, we introduce a perpetual gathering problem and propose a self-stabilizing algorithm for this problem. This problem requires that all non-Byzantine agents always be co-located from a certain time onwards. If the agents know Λ_g and upper bounds N, K, F on n, k, f, the proposed algorithm works in O(K⋅ F⋅ Λ_g⋅ X(N)) rounds, where X(n) is the time required to visit all nodes in a n-nodes network. Our results indicate that while no algorithm can solve the original self-stabilizing gathering problem for any k and f even with exact global knowledge of the network size and the number of agents, the self-stabilizing perpetual gathering problem can always be solved with just upper bounds on this knowledge.

Cite As Get BibTex

Jion Hirose, Ryota Eguchi, and Yuichi Sudo. Self-Stabilizing Weakly Byzantine Perpetual Gathering of Mobile Agents. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.13

Author Details

Jion Hirose
  • Department of Electronics and Information Engineering, National Institute of Technology, Ishikawa College, Ishikawa, Japan
Ryota Eguchi
  • Graduate School of Science and Technology, Nara Institute of Science and Technology, Nara, Japan
Yuichi Sudo
  • Faculty of Computer and Information Sciences, Hosei University, Tokyo, Japan

Funding

  • Hirose, Jion: JSPS KAKENHI Grant Number JP25K03101.
  • Eguchi, Ryota: JSPS KAKENHI Grant Number JP22H03569.
  • Sudo, Yuichi: JST FOREST Program JPMJFR226U and JSPS KAKENHI Grant Numbers JP20KK0232, JP25K03078, and JP25K03079.

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