Improved algorithms for group testing with inhibitors
Information Processing Letters
Guessing secrets efficiently via list decoding
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Adaptive Versus Nonadaptive Attribute-Efficient Learning
Machine Learning
The Algorithmic Complexity of Chemical Threshold Testing
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
On parallel attribute-efficient learning
Journal of Computer and System Sciences
Generalized framework for selectors with applications in optimal group testing
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Group testing for image compression
IEEE Transactions on Image Processing
Separating codes and a new combinatorial search model
Problems of Information Transmission
Improved constructions for non-daptive threshold group testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Reconstruction of hidden graphs and threshold group testing
Journal of Combinatorial Optimization
Threshold and majority group testing
Information Theory, Combinatorics, and Search Theory
Superimposed codes and threshold group testing
Information Theory, Combinatorics, and Search Theory
Group testing with multiple mutually-obscuring positives
Information Theory, Combinatorics, and Search Theory
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We introduce a natural generalization of the well-studied group testing problem: A test gives a positive (negative) answer if the pool contains at least u (at most l) positive elements, and an arbitrary answer if the number of positive elements is between these fixed thresholds l and u. We show that the p positive elements can be determined up to a constant number of misclassifications, bounded by the gap between the thresholds. This is in a sense the best possible result. Then we study the number of tests needed to achieve this goal if n elements are given. If the gap is zero, the complexity is, similarly to classical group testing, O(plogn) for any fixed u. For the general case we propose a two-phase strategy consisting of a Distill and a Compress phase. We obtain some tradeoffs between classification accuracy and the number of tests.