Perpetual exploration in anonymous synchronous networks with a Byzantine black hole

2025-08-11

AI Summary

This paper investigates perpetual exploration in synchronous anonymous multi-agent networks under the presence of a dynamic Byzantine black hole—a malicious entity that may destroy all agents visiting it in each round. As the black hole can disrupt network connectivity, two new problem variants are introduced: pbmPerpExpl (perpetual exploration of some connected component after black hole removal) and pbmPerpExplHome (perpetual exploration of the component containing the initial co-located agents). It presents the first formal model of a variable-malicious black hole without prior topological knowledge and designs cooperative algorithms leveraging face-to-face communication. Theoretical results establish tight bounds: for trees, the problems are optimally solved with 4 and 6 agents, respectively; for general graphs, the minimum number of agents required is tightly bounded below by $2Delta - 1$ and above by $3Delta + 3$, where $Delta$ denotes maximum degree. Key contributions include (i) a novel dynamic black hole model, (ii) a localized perpetual exploration paradigm, and (iii) exact characterization of minimal agent requirements.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Search and Optimization: Heuristic Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper, we investigate: ``How can a group of initially co-located mobile agents perpetually explore an unknown graph, when one stationary node occasionally behaves maliciously, under an adversary's control?'' We call this node a ``Byzantine black hole (BBH)'' and at any given round it may choose to destroy all visiting agents, or none. This subtle power can drastically undermine classical exploration strategies designed for an 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. We thus define two variants: pbmPerpExpl and pbmPerpExplHome. 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 emph{home} node, where agents are initially co-located. Naturally, pbmPerpExplHome is a special case of pbmPerpExpl. Agents operate under a synchronous scheduler and communicate in a face-to-face model. Our goal is to determine the minimum number of agents necessary and sufficient to solve these problems. In acyclic networks, we obtain optimal algorithms that solve pbmPerpExpl with $4$ agents, and pbmPerpExplHome 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 pbmPerpExpl, and an upper bound of $3Δ+3$ agents for pbmPerpExplHome. To our knowledge, this is the first study of a black-hole variant in arbitrary networks without initial topological knowledge.

Problem

• Perpetual exploration in anonymous networks with Byzantine black hole
• Determine minimum agents needed for exploration despite malicious node
• Study exploration variants in acyclic and general graphs without topology knowledge

Innovation

• Mobile agents explore with Byzantine black hole threat
• Optimal agent counts for acyclic and general graphs
• First study in arbitrary networks without topology knowledge