Byzantine gathering in polynomial time

Gathering is a key task in distributed and mobile systems, which becomes significantly harder if some agents are subject to Byzantine faults, known as being the worst ones. We propose here to study the task of Byzantine gathering in an arbitrary graph: despite the presence of Byzantine agents, the g...

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Bibliographic Details
Published in:Distributed computing Vol. 35; no. 3; pp. 235 - 263
Main Authors: Bouchard, Sébastien, Dieudonné, Yoann, Lamani, Anissa
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Complexity
Computer Communication Networks
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Multiagent Systems
Polynomials
Software Engineering/Programming and Operating Systems
Theory of Computation
Mobile agent
Gathering
Deterministic algorithm
Byzantine fault
Polynomial time
ISSN:0178-2770, 1432-0452
Online Access:Get full text
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Summary:Gathering is a key task in distributed and mobile systems, which becomes significantly harder if some agents are subject to Byzantine faults, known as being the worst ones. We propose here to study the task of Byzantine gathering in an arbitrary graph: despite the presence of Byzantine agents, the goal is to ensure that all the other (good) agents, executing the same algorithm, eventually meet at the same node and stop. Initially, each agent gets as input a different label and some global knowledge that is common to all agents. The agents move in synchronous rounds and communicate with each other only when located at the same node. There are f Byzantine agents. These agents act in an unpredictable way, e.g., they may convey arbitrary informations or forge any label. In the literature, the gathering algorithms working in such a context all have an exponential time complexity in the number n of nodes and the labels of the good agents. In this paper, we design a deterministic algorithm to solve Byzantine gathering in time polynomial in n and the logarithm ℓ of the smallest label of a good agent, provided the agents are a strong team i.e., a team where the number of good agents is at least some quadratic polynomial in f . Our algorithm requires global knowledge that can be coded in O ( log log log n ) bits: we prove this size is of optimal order of magnitude to obtain a polynomial time complexity in n and ℓ with strong teams.
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ISSN:0178-2770
1432-0452
DOI:10.1007/s00446-022-00419-9