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arXiv · 2408.10757

Decreasing verification radius in local certification

Laurent Feuilloley·Jan Janoušek·Jan Matyáš Křišťan·Josef Erik Sedláček
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Abstract

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.

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Laurent Feuilloley, Jan Janoušek, Jan Matyáš Křišťan, Josef Erik Sedláček. 2024-08-20. Decreasing verification radius in local certification. https://arxiv.org/abs/2408.10757

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