Approximate proof-labeling schemes

Keren Censor-Hillel*, Ami Paz, Mor Perry

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study a new model of verification of boolean predicates over distributed networks. Given a network configuration, the proof-labeling scheme (PLS) model defines a distributed proof in the form of a label that is given to each node, and all nodes locally verify that the network configuration satisfies the desired boolean predicate by exchanging labels with their neighbors. The proof size of the scheme is defined to be the maximum size of a label. In this work, we extend this model by defining the approximate proof-labeling scheme (APLS) model. In this new model, the predicates for verification are of the form ψ ≤ φ, where ψ, φ: F → ℕ for a family of configurations F. Informally, the predicates considered in this model are a comparison between two values of the configuration. As in the PLS model, nodes exchange labels in order to locally verify the predicate, and all must accept if the network satisfies the predicate. The soundness condition is relaxed with an approximation ration α, so that only if ψ > αφ some node must reject. We show that in the APLS model, the proof size can be much smaller than the proof size of the same predicate in the PLS model . Moreover, we prove that there is a tradeoff between the approximation ratio and the proof size.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 24th International Colloquium, SIROCCO 2017, Revised Selected Papers
EditorsShantanu Das, Sebastien Tixeuil
PublisherSpringer Verlag
Number of pages19
ISBN (Print)9783319720494
StatePublished - 2017
Event24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017 - Porquerolles, France
Duration: 19 Jun 201722 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10641 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017


  • Approximation algorithms
  • Distributed graph algorithms
  • Distributed verification
  • Primal-dual algorithms


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