The algorithmic aspects of the regularity lemma
Journal of Algorithms
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Testing subgraphs in directed graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Efficient Testing of Large Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Journal of Algorithms
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
Three Theorems Regarding Testing Graph Properties
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Testing subgraphs in directed graphs
Journal of Computer and System Sciences - Special issue: STOC 2003
Linear equations, arithmetic progressions and hypergraph property testing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Testing triangle-freeness in general graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Testing whether a digraph contains H-free k-induced subgraphs
Theoretical Computer Science
Streaming and communication complexity of clique approximation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Let H be a fixed graph on h vertices. We say that a graph G is induced H-free if it does not contain any induced copy of H. Let G be a graph on n vertices and suppose that at least εn2 edges have to be added to or removed from it in order to make it induced H-free. It was shown in [5] that in this case G contains at least f(ε, h)nh induced copies of H, where 1/f(ε, h) is an extremely fast growing function in 1/ε, that is independent of n. As a consequence, it follows that for every H, testing induced H-freeness with one-sided error has query complexity independent of n. A natural question, raised by the first author in [1], is to decide for which graphs H the function 1/f(ε, H) can be bounded from above by a polynomial in 1/ε. An equivalent question is for which graphs H, can one design a one-sided error property tester for testing induced H-freeness, whose query complexity is polynomial in 1/ε. We settle this question almost completely by showing that, quite surprisingly, for any graph other than the paths of lengths 1,2 and 3, the cycle of length 4, and their complements, no such property tester exists. We further show that a similar result also applies to the case of directed graphs, thus answering a question raised by the authors in [9]. We finally show that the same results hold even in the case of two-sided error property testers. The proofs combine combinatorial, graph theoretic and probabilistic arguments with results from additive number theory.