Introduction to local certification

Abstract

Local certification is an concept that has been defined and studied recently by the distributed computing community. It is the following mechanism, known under various names such as distributed verification, distributed proof or proof-labeling scheme. The nodes of a graph want to decide collectively whether the graph has some given property, but they only know a local neighborhood, e.g. their neighbors in the graph. The nodes are then given a distributed proof that certifies that the graph has the property, and they have to collectively check that this proof is correct.We believe that local certification is a concept that anyone interested in algorithms or graphs could be interested in. This document is an introduction to this domain, that does not require any knowledge of distributed computing. It also contains a review of the recent works and a list of open problems.Note. This document can be seen as a complement to the survey [17]. The two texts differ by their target audience: unlike this text which is an invitation to the topic, [17] is a comprehensive structured survey aimed at researchers in distributed computing. For this reason, we use less citations, but more proof sketches, pictures and arguably more musing. lolita first sentence The two first sections are based on the introduction of the PhD thesis of the author [14]. The last section about current research directions is new. Comments are most welcome.