Article Dans Une Revue Theoretical Computer Science Année : 2025

Decreasing verification radius in local certification

Résumé

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 neighborhood 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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hal-05370178 , version 1 (18-11-2025)

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Laurent Feuilloley, Jan Janoušek, Jan Matyáš Křišťan, Josef Erik Sedláček. Decreasing verification radius in local certification. Theoretical Computer Science, 2025, 1056, pp.115520. ⟨10.1016/j.tcs.2025.115520⟩. ⟨hal-05370178⟩
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