Self-testing/correcting with applications to numerical problems
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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)
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
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-Preserving data reconstruction
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Distributed discovery of large near-cliques
Proceedings of the 28th ACM symposium on Principles of distributed computing
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Distributed discovery of large near-cliques
DISC'09 Proceedings of the 23rd international conference on Distributed computing
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
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We investigate the problem of monotonicity reconstruction, as defined in [3], in a parallel setting. We have oracle access to a nonnegative real-valued function f defined on domain [n]d = {1,…,n}d. 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 ∈ [n]d outputs the value of g(x), and runs in time that is highly sublinear 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 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 the distance of the approximating function g from f is at most a constant multiple of the minimum distance of any monotone function from f. This implementation allows for parallelization: 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.