Black Hole Search Despite Byzantine Agents

Abstract

We study the black hole search problem of k mobile agents in synchronous Byzantine environments. The goal of the black hole search problem is to detect a black hole node, which deletes all agents visiting the node without any trace. We assume that the graph topology is arbitrary, each agent has a unique ID, and at most \(f_u\) strongly Byzantine agents exist. Under these assumptions, we propose an algorithm that detects a black hole node in \(O(f_u n)\) rounds when \(k \ge 2f_u+2\) holds, where n is the number of nodes. We also show that it is impossible to solve the black hole search problem when \(k \le 2c_u +1\) holds, where \(c_u\) is an upper bound of the number of crash agents. Since a crash fault is a special case of a Byzantine fault, the above result also applies to strongly Byzantine agents. This implies that our proposed algorithm is optimal in terms of the number of tolerable faulty agents. To the best of our knowledge, this is the first work to address the black hole search problem with Byzantine agents.