Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic Aspects of Property Testing in the Dense Graphs Model
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
The structure of almost all graphs in a hereditary property
Journal of Combinatorial Theory Series B
Algorithmic aspects of property testing in the dense graphs model
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Algorithmic Aspects of Property Testing in the Dense Graphs Model
SIAM Journal on Computing
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Alon et. al. [N. Alon, E. Fischer, M. Krivelevich, and M. Szegedy, Combinatorica, 20 (2000), pp. 451-476] showed that every property that is characterized by a finite collection of forbidden induced subgraphs is $\epsilon$-testable. However, the complexity of the test is double-tower with respect to $1/\epsilon$, as the only tool known to construct such tests uses a variant of Szemerédi's regularity lemma. Here we show that any property of bipartite graphs that is characterized by a finite collection of forbidden induced subgraphs is $\epsilon$-testable, with a number of queries that is polynomial in $1/\epsilon$. Our main tool is a new “conditional” version of the regularity lemma for binary matrices, which may be interesting on its own.