The algorithmic aspects of the regularity lemma
Journal of Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Extremal problems on set systems
Random Structures & Algorithms
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Efficient Testing of Large Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Property testing and its connection to learning and approximation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Testing Subgraphs in Large Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Regularity properties for triple systems
Random Structures & Algorithms
Linear equations, arithmetic progressions and hypergraph property testing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An Algorithmic Version of the Hypergraph Regularity Method
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The counting lemma for regular k-uniform hypergraphs
Random Structures & Algorithms
Property testing in hypergraphs and the removal lemma
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Testing monotonicity over graph products
Random Structures & Algorithms
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
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We investigate a basic problem in combinatorial property testing, in the sense of Goldreich, Goldwasser, and Ron [9,10], in the context of 3-uniform hypergraphs, or 3-graphs for short. As customary, a 3-graph F is simply a collection of 3-element sets. Let Forbind(n, F) be the family of all 3-graphs on n vertices that contain no copy of F as an induced subhypergraph. We show that the property "H 驴 Forbind(n, F)" is testable, for any 3-graph F. In fact, this is a consequence of a new, basic combinatorial lemma, which extends to 3-graphs a result for graphs due to Alon, Fischer, Krivelevich, and Szegedy [2,3].Indeed, we prove that if more than 驴n3 (驴 0) triples must be added or deleted from a 3-graph H on n vertices to destroy all induced copies of F, then H must contain 驴 cn |V(F)| induced copies of F, as long as n 驴 n0(驴,F). Our approach is inspired in [2,3], but the main ingredients are recent hypergraph regularity lemmas and counting lemmas for 3-graphs.