An early termination strategy for the distributed biased min-consensus protocol under disturbances

The distributed biased min-consensus (DBMC) protocol is an iterative scheme that solves the shortest path problem asymptotically, requiring only local information exchange between neighboring nodes. By appropriately designing the gain function, prior work [1] proposed a DBMC-based system that ensures convergence within a pre-specified time interval. However, this guarantee assumes the absence of disturbances. In this paper, we study the DBMC-based system under disturbances affecting the edge weights. We first establish rigorous error bounds on the resulting state estimates. Building on this analysis, we then propose a practical early termination strategy to prevent potential singularities, specifically, unbounded gain, that may arise in the presence of disturbances, while still ensuring that the shortest paths are correctly identified.Simulations are performed to validate and illustrate the theoretical results.