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SIAM Journal on Computing
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
Testing juntas: a brief survey
Property testing
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Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Testing juntas: a brief survey
Property testing
Introduction to testing graph properties
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Introduction to testing graph properties
Studies in complexity and cryptography
Contemplations on testing graph properties
Studies in complexity and cryptography
Algorithmic Aspects of Property Testing in the Dense Graphs Model
SIAM Journal on Computing
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We consider the question of whether adaptivity can improve the complexity of property testing algorithms in the dense graphsmodel. It is known that there can be at most a quadratic gap between adaptive and non-adaptive testers in this model, but it was not known whether any gap indeed exists. In this work we reveal such a gap.Specifically, we focus on the well studied property of bipartiteness. Bogdanov and Trevisan (IEEE Symposium on Computational Complexity, 2004) proved a lower bound of 茂戮驴(1/茂戮驴2) on the query complexity of non-adaptivetesting algorithms for bipartiteness. This lower bound holds for graphs with maximum degree O(茂戮驴n). Our main result is an adaptivetesting algorithm for bipartiteness of graphs with maximum degree O(茂戮驴n) whose query complexity is $\tilde{O}(1/\epsilon^{3/2})$. A slightly modified version of our algorithm can be used to test the combined property of being bipartite and having maximum degree O(茂戮驴n). Thus we demonstrate that adaptive testers are stronger than non-adaptive testers in the dense graphs model.We note that the upper bound we obtain is tight up-to polylogarithmic factors, in view of the 茂戮驴(1/茂戮驴3/2) lower bound of Bogdanov and Trevisan for adaptivetesters. In addition we show that $\tilde{O}(1/\epsilon^{3/2})$ queries also suffice when (almost) all vertices have degree $\Omega(\sqrt \epsilon \cdot n)$. In this case adaptivity is not necessary.