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Perpetual Exploration in Anonymous Synchronous Networks with a Byzantine Black Hole

Authors Adri Bhattacharya , Pritam Goswami , Evangelos Bampas , Partha Sarathi Mandal

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Design and analysis of algorithms
Keywords
  • mobile agents
  • perpetual exploration
  • malicious host
  • Byzantine black hole

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Abstract

In this paper, we investigate the following question: 
"How can a group of initially co-located mobile agents perpetually explore an unknown graph, when one stationary node occasionally behaves maliciously, under the control of an adversary?"
This malicious node is termed as "Byzantine black hole (BBH)" and at any given round it may choose to destroy all visiting agents, or none of them. While investigating this question, we found out that this subtle power turns out to drastically undermine even basic exploration strategies which have been proposed in the context of a classical, always active, black hole.
We study this perpetual exploration problem in the presence of at most one BBH, without initial knowledge of the network size. Since the underlying graph may be 1-connected, perpetual exploration of the entire graph may be infeasible. Accordingly, we define two variants of the problem, termed as PerpExploration-BBH and PerpExploration-BBH-Home. In the former, the agents are tasked to perform perpetual exploration of at least one component, obtained after the exclusion of the BBH. In the latter, the agents are tasked to perform perpetual exploration of the component which contains the home node, where agents are initially co-located. Naturally, PerpExploration-BBH-Home is a special case of PerpExploration-BBH. The mobile agents are controlled by a synchronous scheduler, and they communicate via face-to-face model of communication.
The main objective in this paper is to determine the minimum number of agents necessary and sufficient to solve these problems. We first consider the problems in acyclic networks, and we obtain optimal algorithms that solve PerpExploration-BBH with 4 agents, and PerpExploration-BBH-Home with 6 agents in trees. The lower bounds hold even in path graphs. In general graphs, we give a non-trivial lower bound of 2Δ-1 agents for PerpExploration-BBH, and an upper bound of 3Δ+3 agents for PerpExploration-BBH-Home. To the best of our knowledge, this is the first paper that studies a variant of a black hole in arbitrary networks, without initial topological knowledge about the network.

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Adri Bhattacharya, Pritam Goswami, Evangelos Bampas, and Partha Sarathi Mandal. Perpetual Exploration in Anonymous Synchronous Networks with a Byzantine Black Hole. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.16

Author Details

Adri Bhattacharya
  • Indian Institute of Technology Guwahati, Assam, India
Pritam Goswami
  • Sister Nivedita University, Kolkata, India
Evangelos Bampas
  • Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400 Orsay, France
Partha Sarathi Mandal
  • Indian Institute of Technology Guwahati, Assam, India

Funding

  • Bhattacharya, Adri: Supported by CSIR, Govt. of India, Grant Number: 09/731(0178)/2020- EMR-I.

Acknowledgements

We thank the DISC 2025 reviewers for their careful reading and useful feedback.

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