TY - JOUR

T1 - Approximate proof-labeling schemes

AU - Censor-Hillel, Keren

AU - Paz, Ami

AU - Perry, Mor

N1 - Publisher Copyright:
© 2018

PY - 2020/4/2

Y1 - 2020/4/2

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 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.

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 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.

KW - Approximation algorithms

KW - Distributed graph algorithms

KW - Distributed verification

KW - Primal-dual algorithms

UR - http://www.scopus.com/inward/record.url?scp=85052750866&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2018.08.020

DO - 10.1016/j.tcs.2018.08.020

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AN - SCOPUS:85052750866

SN - 0304-3975

VL - 811

SP - 112

EP - 124

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -