A local t-diagnosis algorithm for corruption detection on networks

In an era where networks are crucial to the functioning of critical infrastructure, the ability to quickly and accurately identify compromised nodes using only local information is essential. This research aims to integrate insights from the SPMC model and corruption detection frameworks, proposing a novel algorithm that allows nodes to autonomously assess their status based on localized interactions. The SPMC model, an extension of the PMC model, is derived by introducing two key assumptions: (1) each adjacent node pair is assumed to be mutually tested; and (2) in one-step diagnosis, only the minimal consistent fault set corresponding to a given syndrome is identified. In this paper, we propose a diagnosis algorithm based on local diagnosis techniques to efficiently evaluate the state of a vertex in the system. The algorithm is proven to be correct and is not reliant on any structural assumptions or conjectures, making it applicable to any network. Furthermore, we demonstrate the application of our results to the hypercube Q<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf>.