Byzantine-Tolerant Gathering of Mobile Agents in Asynchronous Arbitrary Networks with Authenticated Whiteboards

Abstract

We propose two algorithms for the gathering of k mobile agents in asynchronous Byzantine environments. For both algorithms, we assume that graph topology is arbitrary, each node is equipped with an authenticated whiteboard, agents have unique IDs, and at most f weakly Byzantine agents exist. Here, a weakly Byzantine agent can make arbitrary behavior except falsifying its ID. Under these assumptions, the first algorithm achieves a gathering without termination detection in O(m+fn) moves per agent (m is the number of edges and n is the number of nodes). The second algorithm achieves a gathering with termination detection in O(m+fn) moves per agent by additionally assuming that agents on the same node are synchronized, $f<\lceil \frac{1}{3} k \rceil$ holds, and agents know k. To the best of our knowledge, this is the first work to address the gathering problem of mobile agents for arbitrary topology networks in asynchronous Byzantine environments.