Approximate proof-labeling schemes

Keren Censor-Hillel, Ami Paz*, Mor Perry

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 focus on two verification problems: upper and lower bounds on the diameter of the graph, and the maximality of a given matching. For these problems, we present the first results that apply to all graph structures. In our new APLS model, we show that 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. Finally, we present the first general result for maximum cardinality matching in the PLS model.

Original languageEnglish
Pages (from-to)112-124
Number of pages13
JournalTheoretical Computer Science
StatePublished - 2 Apr 2020


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


Dive into the research topics of 'Approximate proof-labeling schemes'. Together they form a unique fingerprint.

Cite this