Twenty-Two New Approximate Proof Labeling Schemes (Full Version)

TL;DR

This paper introduces twenty-two new approximate proof labeling schemes (APLS) that enable efficient verification of graph properties with relaxed correctness criteria, improving upon traditional proof labeling schemes.

Contribution

The paper presents twenty-two novel APLS constructions that extend proof labeling schemes to allow approximate verification, addressing limitations of previous exact schemes.

Findings

Twenty-two new APLS constructions introduced

Enhanced verification efficiency for graph properties

Relaxed correctness criteria enable broader applicability

Abstract

Introduced by Korman, Kutten, and Peleg (Distributed Computing 2005), a \emph{proof labeling scheme (PLS)} is a system dedicated to verifying that a given configuration graph satisfies a certain property. It is composed of a centralized \emph{prover}, whose role is to generate a proof for yes-instances in the form of an assignment of labels to the nodes, and a distributed \emph{verifier}, whose role is to verify the validity of the proof by local means and accept it if and only if the property is satisfied. To overcome lower bounds on the label size of PLSs for certain graph properties, Censor-Hillel, Paz, and Perry (SIROCCO 2017) introduced the notion of an \emph{approximate proof labeling scheme (APLS)} that allows the verifier to accept also some no-instances as long as they are not "too far" from satisfying the property.