Nondeterministic graph property testing
TL;DR: This paper studies certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs, and proves that non-deterministically testable properties are also deterministicallyTestable.
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Abstract: A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that nondeterministically testable properties are also deterministically testable.
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Citations
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Property Testing and its connection to Learning and Approximation
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Limits of locally–globally convergent graph sequences
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Non-interactive proofs of proximity
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TL;DR: In this article, a study of non-interactive proofs of proximity is presented, where the verifier is only assured of the proximity of a given statement to a correct one by rejecting inputs that are far from being valid.
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Non-Interactive Proofs of Proximity.
Tom Gur,Ron D. Rothblum +1 more
TL;DR: In this article, a study of non-interactive proofs of proximity is presented, where the verifier is only assured of the proximity of a given statement to a correct one by rejecting inputs that are far from being valid.
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Testing Graph Clusterability: Algorithms and Lower Bounds
Ashish Chiplunkar,Michael Kapralov,Sanjeev Khanna,Aida Mousavifar,Yuval Peres +4 more
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TL;DR: In this article, Czumaj, Peng, and Sohler gave a sublinear time algorithm for testing k-clusterability in time O(n^1/2 poly(k)).
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References
•Book
Large Networks and Graph Limits
László Lovász
- 12 Dec 2012
TL;DR: Laszlo Lovasz has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks.
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Limits of dense graph sequences
László Lovász,Balázs Szegedy +1 more
TL;DR: It is shown that if a sequence of dense graphs G has the property that for every fixed graph F, the density of copies of F in G"n tends to a limit, then there is a natural ''limit object,'' namely a symmetric measurable function W:[0,1]^2->[0, 1].
Robust Characterizations of Polynomials withApplications to Program Testing
Ronitt Rubinfeld,Madhu Sudan +1 more
TL;DR: The characterizations provide results in the area of coding theory by giving extremely fast and efficient error-detecting schemes for some well-known codes and play a crucial role in subsequent results on the hardness of approximating some NP-optimization problems.
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•Journal Article
Property Testing and its connection to Learning and Approximation
TL;DR: In this paper, the authors consider the question of determining whether a function f has property P or is e-far from any function with property P. In some cases, it is also allowed to query f on instances of its choice.
873