Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
STOC '01 Proceedings of the thirty-third 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
Testing the diameter of graphs
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Efficient Testing of Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Regular Languages are Testable with a Constant Number of Queries
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
On the strength of comparisons in property testing
Information and Computation
Journal of Computer and System Sciences - Special issue on FOCS 2002
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Distribution-Free Property-Testing
SIAM Journal on Computing
A lower bound for distribution-free monotonicity testing
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Monotonicity testing and shortest-path routing on the cube
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local Monotonicity Reconstruction
SIAM Journal on Computing
Local property reconstruction and monotonicity
Property testing
Local property reconstruction and monotonicity
Property testing
A o(n) monotonicity tester for boolean functions over the hypercube
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Optimal bounds for monotonicity and lipschitz testing over hypercubes and hypergrids
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider the problem of monotonicity testing over graph products. Monotonicity testing is one of the central problems studied in the field of property testing. We present a testing approach that enables us to use known monotonicity testers for given graphs G1, G2, to test monotonicity over their product G1 × G2. Such an approach of reducing monotonicity testing over a graph product to monotonicity testing over the original graphs, has been previously used in the special case of monotonicity testing over [n]d for a limited type of testers; in this article, we show that this approach can be applied to allow modular design of testers in many interesting cases: this approach works whenever the functions are boolean, and also in certain cases for functions with a general range. We demonstrate the usefulness of our results by showing how a careful use of this approach improves the query complexity of known testers. Specifically, based on our results, we provide a new analysis for the known tester for [n]d which significantly improves its query complexity analysis in the low-dimensional case. For example, when d = O(1), we reduce the best known query complexity from O(log 2n-ε) to O(log n-ε). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 An extended abstract of this paper appeared in ICALP 2004 [23].