When Agents are Powerful: Black Hole Search in Time-Varying Graphs
Tanvir Kaur, Ashish Saxena
TL;DR
The paper investigates Black Hole Search on time-varying graphs under strengthened agent capabilities. It introduces global communication and 1-hop visibility, and refines the 1-BHS objective to require locating a neighboring node and identifying the exact port to the black hole $v_{BH}$. It proves tight impossibility results for small agent counts and provides two optimal algorithms: a 1-BHS solution with four agents using 1-hop visibility and local communication, and a robust solution with $\delta_{BH}+2$ agents using global communication. Together, these results quantify how enhanced communication and visibility reduce agent requirements and yield concrete time and memory bounds for locating $v_{BH}$ in dynamic networks.
Abstract
A black hole is a harmful node in a graph that destroys any resource entering it, making its identification a critical task. In the \emph{Black Hole Search (BHS)} problem, a team of agents operates on a graph $G$ with the objective that at least one agent must survive and correctly identify an edge incident to the black hole. Prior work has addressed BHS in arbitrary dynamic graphs under the restrictive \emph{face-to-face} communication, where agents can exchange information only when co-located. This constraint significantly increases the number of agents required to solve the problem. In this work, we strengthen the capabilities of agents in two ways: (i) granting them \emph{global communication}, enabling interaction regardless of location, and (ii) equipping them with \emph{1-hop visibility}, allowing each agent to observe its immediate neighborhood. These enhancements lead to more efficient solutions for the BHS problem in dynamic graphs.