Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
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
Randomized algorithms
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
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
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
On the strength of comparisons in property testing
Information and Computation
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Estimating the distance to a monotone function
Random Structures & Algorithms
Testing versus Estimation of Graph Properties
SIAM Journal on Computing
Parallel monotonicity reconstruction
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Testing monotonicity over graph products
Random Structures & Algorithms
Property-Preserving Data Reconstruction
Algorithmica
Noise Tolerance of Expanders and Sublinear Expander Reconstruction
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
Testability and repair of hereditary hypergraph properties
Random Structures & Algorithms
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
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 property reconstruction and monotonicity
Property testing
Local property reconstruction and monotonicity
Property testing
Steiner transitive-closure spanners of low-dimensional posets
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Space-efficient local computation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We investigate the problem of monotonicity reconstruction, as defined by Ailon et al. (2004) in a localized setting. We have oracle access to a nonnegative real-valued function $f$ defined on the domain $[n]^d=\{1,\dots,n\}^d$ (where $d$ is viewed as a constant). We would like to closely approximate $f$ by a monotone function $g$. This should be done by a procedure (a filter) that given as input a point $x\in[n]^d$ outputs the value of $g(x)$, and runs in time that is polylogarithmic in $n$. The procedure can (indeed must) be randomized, but we require that all of the randomness be specified in advance by a single short random seed. We construct such an implementation where the time and space per query is $(\log n)^{O(1)}$ and the size of the seed is polynomial in $\log n$ and $d$. Furthermore, with high probability, the ratio of the (Hamming) distance between $g$ and $f$ to the minimum possible Hamming distance between a monotone function and $f$ is bounded above by a function of $d$ (independent of $n$). This allows for a local implementation: one can initialize many copies of the filter with the same short random seed, and they can autonomously handle queries, while producing outputs that are consistent with the same approximating function $g$.