Information theory in property testing and monotonicity testing in higher dimension

Authors:
Nir Ailon;Bernard Chazelle
Affiliations:
Ben Gurion University of the Negev, Department of Electrical and Computer Engineering, Beer Sheva, Israel and Department of Computer Science, Princeton University, Princeton, NJ;Department of Computer Science, Princeton University, Princeton, NJ
Venue:
Information and Computation
Year:
2006

Citing 6
Cited 15

Spot-checkers

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation

Journal of the ACM (JACM)
Monotonicity testing over general poset domains

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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
Testing Juntas

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the strength of comparisons in property testing

Information and Computation

Testing monotonicity over graph products

Random Structures & Algorithms
Distribution-Free Testing Lower Bounds for Basic Boolean Functions

APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Transitive-closure spanners

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete 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
Property testing: a learning theory perspective

COLT'07 Proceedings of the 20th annual conference on Learning theory
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
Transitive-closure spanners: a survey

Property testing
Local property reconstruction and monotonicity

Property testing
Transitive-closure spanners: a survey

Property testing
Local property reconstruction and monotonicity

Property testing
Sublinear Time Algorithms

SIAM Journal on Discrete Mathematics
Optimal bounds for monotonicity and lipschitz testing over hypercubes and hypergrids

Proceedings of the forty-fifth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In property testing, we are given oracle access to a function f, and we wish to test if the function satisfies a given property P, or it is ε-far from having that property. In a more general setting, the domain on which the function is defined is equipped with a probability distribution, which assigns different weight to different elements in the domain. This paper relates the complexity of testing the monotonicity of a function over the d-dimensional cube to the Shannon entropy of the underlying distribution. We provide an improved upper bound on the query complexity of the property tester.