When Agents are Powerful: Black Hole Search in Time-Varying Graphs

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.