How to locally certify a global property?
From spanning trees to planar graphs, and beyond.
Local certification is a mechanism that enables the nodes of a network to locally check that a global property holds. It originates from the study of fault-tolerance, and in particular from self-stabilization, where it is crucial to be able to detect that a solution has been corrupted. In this talk, I will introduce this notion, describe an essential result in the area which is the certification of a spanning tree, and give a quick overview of the current research and future challenges.