This paper deals with local certification, specifically locally checkable proofs: given a graph property, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done locally without the knowledge of the whole graph. More precisely, a distributed algorithm, called a verifier, is executed on each vertex. The verifier observes the local neighborhood up to a constant distance and either accepts or rejects. We examine the trade-off between the visibility radius and the size of certificates. We describe a procedure that decreases the radius by encoding the neighbourhood of each vertex into its certificate. We also provide a corresponding lower bound on the required certificate size increase, showing that such an approach is close to optimal.
@article{arxiv.2408.10757,
title = {Decreasing verification radius in local certification},
author = {Laurent Feuilloley and Jan Janoušek and Jan Matyáš Křišťan and Josef Erik Sedláček},
journal= {arXiv preprint arXiv:2408.10757},
year = {2024}
}