Max-Consensus with Deterministic Convergence in Directed Graphs with Unreliable Communication Links

Abstract

We present DMaC, a novel distributed, finite-time algorithm that guarantees max-consensus in directed networks with unreliable communication links experiencing packet drops. Unlike existing methods, DMaC ensures all nodes compute the exact maximum state under arbitrary packet loss patterns. It incorporates a fully distributed termination mechanism, enabling nodes to autonomously determine whether convergence has occurred. Our algorithm leverages narrowband error-free feedback channels to acknowledge successful (single-bit) transmissions with minimal communication overhead. We analyze our algorithm's operation, and we provide a convergence proof establishing explicit bounds on the required time steps. We validate its correctness in a wireless sensor network for environmental monitoring, and finally, we compare against existing approaches highlighting our algorithm's operational advantages.