TY - GEN

T1 - Approximate proof-labeling schemes

AU - Censor-Hillel, Keren

AU - Paz, Ami

AU - Perry, Mor

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Distributed graph algorithms

KW - Distributed verification

KW - Primal-dual algorithms

UR - http://www.scopus.com/inward/record.url?scp=85040125233&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-72050-0_5

DO - 10.1007/978-3-319-72050-0_5

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AN - SCOPUS:85040125233

SN - 9783319720494

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 71

EP - 89

BT - Structural Information and Communication Complexity - 24th International Colloquium, SIROCCO 2017, Revised Selected Papers

A2 - Das, Shantanu

A2 - Tixeuil, Sebastien

PB - Springer Verlag

T2 - 24th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2017

Y2 - 19 June 2017 through 22 June 2017

ER -