Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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
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
Fast Approximate PCPs for Multidimensional Bin-Packing Problems
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
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
Simple Analysis of Graph Tests for Linearity and PCP
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Functions that have Read-Twice Constant Width Branching Programs are not Necessarily Testable
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
On Testing Convexity and Submodularity
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Algorithms column: sublinear time algorithms
ACM SIGACT News
On the strength of comparisons in property testing
Information and Computation
A characterization of easily testable induced subgraphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Sublinear algorithms for testing monotone and unimodal distributions
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue on FOCS 2002
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
Conformance testing in the presence of multiple faults
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
A Characterization of Easily Testable Induced Subgraphs
Combinatorics, Probability and Computing
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating the distance to a monotone function
Random Structures & Algorithms
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
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
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
A large lower bound on the query complexity of a simple boolean function
Information Processing Letters
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Testing convexity properties of tree colorings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Testing Boolean function isomorphism
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Detecting and exploiting near-sortedness for efficient relational query evaluation
Proceedings of the 14th International Conference on Database Theory
SIAM Journal on Computing
Local Monotonicity Reconstruction
SIAM Journal on Computing
Property testing of massively parametrized problems – a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Property testing
Local property reconstruction and monotonicity
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Transitive-closure spanners: a survey
Property testing
Property testing
Local property reconstruction and monotonicity
Property testing
Lower bounds for testing computability by small width OBDDs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On the communication and streaming complexity of maximum bipartite matching
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
Information theory in property testing and monotonicity testing in higher dimension
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Property testing and the branching program size of boolean functions
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Nearly complete graphs decomposable into large induced matchings and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
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
An algebraic characterization of testable boolean CSPs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The field of property testing studies algorithms that distinguish, using a small number of queries, between inputs which satisfy a given property, and those that are `far' from satisfying the property. Testing properties that are defined in terms of monotonicity has been extensively investigated, primarily in the context of the monotonicity of a sequence of integers, or the monotonicity of a function over the n-dimensional hypercube {1,&ldots;,m}n. These works resulted in monotonicity testers whose query complexity is at most polylogarithmic in the size of the domain.We show that in its most general setting, testing that Boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory. These problems include: testing that a Boolean assignment of variables is close to an assignment that satisfies a specific 2-CNF formula, testing that a set of vertices is close to one that is a vertex cover of a specific graph, and testing that a set of vertices is close to a clique.We then investigate the query complexity of monotonicity testing of both Boolean and integer functions over general partial orders. We give algorithms and lower bounds for the general problem, as well as for some interesting special cases. In proving a general lower bound, we construct graphs with combinatorial properties that may be of independent interest.