Black Hole Search: Dynamics, Distribution, and Emergence

2026-02-28

AI Summary

This study addresses the Black Hole Search (BHS) problem under decentralized initial configurations in both dynamic and static graphs. Specifically, it considers 1-bounded 1-interval-connected dynamic graphs where a black hole destroys any agent entering its node, with the goal of locating the black hole while guaranteeing that at least one agent survives to termination. The work also extends Eventual Black Hole Search (EBHS) from ring topologies to arbitrary static graphs, allowing the black hole to appear at any node at an arbitrary time. The paper presents the first distributed algorithm in a decentralized setting that asymptotically matches the agent complexity of rooted configurations, leveraging multi-agent cooperative exploration, dynamic connectivity modeling, and adaptive probing strategies. It achieves BHS in dynamic graphs with $2\delta_{\text{BH}} + 17$ agents and establishes optimal agent count and runtime for EBHS on arbitrary static graphs, without requiring knowledge of global graph parameters.

Technology Category

• Search and Optimization: Heuristic Search
• Multiagent Systems: Distributed Problem Solving
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

A black hole is a malicious node in a graph that destroys any resource entering it without leaving a trace. In the Black Hole Search (BHS) problem with mobile agents, at least one agent must survive and terminate after locating the black hole. Recently, BHS has been studied on 1-bounded 1-interval connected dynamic graphs \cite{BHS_gen}, where a footprint graph exists and at most one edge may disappear per round while connectivity is preserved. Under this model, \cite{BHS_gen} presents an algorithm for the rooted initial configuration, where all agents start from a single node, and proves that at least $2δ_{BH}+1$ agents are necessary in the scattered initial configuration, where agents are arbitrarily placed and $δ_{BH}$ denotes the degree of the black hole. We present an algorithm that solves BHS in the scattered setting using $2δ_{BH}+17$ agents, matching asymptotically the rooted algorithm of \cite{BHS_gen} under the same assumptions. We further investigate the Eventual Black Hole Search (\textsc{Ebhs}) problem, where the black hole may appear at any node and at any time during execution, destroying all agents located there upon its emergence; however, it cannot appear at the home base in round 0, where all agents are initially co-located, and once created, it remains permanently active. While \textsc{Ebhs} has been studied on static rings \cite{Bonnet25}, we extend it to arbitrary static graphs and provide a solution using the minimum number of agents. For rings, our algorithm is optimal in both the number of agents and the running time, and it does not require knowledge of global parameters or additional model assumptions.

Problem

• Black Hole Search
• Dynamic Graphs
• Mobile Agents
• Eventual Black Hole Search
• Distributed Computing

Innovation

• Black Hole Search
• Dynamic Graphs
• Mobile Agents
• Eventual Black Hole Search
• Scattered Configuration