On the upper bound of the size of the r-cover-free families
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
Non-adaptive group testing in the presence of errors
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Lower bounds for identifying subset members with subset queries
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Explicit constructions of selectors and related combinatorial structures, with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Tight bounds for depth-two superconcentrators
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Optimal Two-Stage Algorithms for Group Testing Problems
SIAM Journal on Computing
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes
SIAM Journal on Computing
Almost optimal explicit selectors
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
IEEE Transactions on Information Theory
Efficiently decodable non-adaptive group testing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved constructions for non-daptive threshold group testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Superselectors: efficient constructions and applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Efficiently decodable error-correcting list disjunct matrices and applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
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We study combinatorial group testing schemes for learning d-sparse boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we give a general framework for construction of highly noise-resilient group testing schemes using randomness condensers. Simple randomized instantiations of this construction give non-adaptive measurement schemes, with m = O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of δm false positives and Ω(m/d) false negatives within the measurement outcomes, for any constant δ m = O(d1+o(1) log n) measurements. We also obtain explicit constructions that allow fast reconstruction in time poly(m), which would be sublinear in n for sufficiently sparse vectors.