Randomized algorithms
Selective families, superimposed codes, and broadcasting on unknown radio networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Improved Results for Competitive Group Testing
Combinatorics, Probability and Computing
Algorithm Design
What's hot and what's not: tracking most frequent items dynamically
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
Optimal Two-Stage Algorithms for Group Testing Problems
SIAM Journal on Computing
Note: Exploring the missing link among d-separable, d-separable and d-disjunct matrices
Discrete Applied Mathematics
Improved Combinatorial Group Testing Algorithms for Real-World Problem Sizes
SIAM Journal on Computing
Bounds for nonadaptive group tests to estimate the amount of defectives
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Group Testing With Random Pools: Optimal Two-Stage Algorithms
IEEE Transactions on Information Theory
New and improved BIST diagnosis methods from combinatorial Group testing theory
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The classical group testing problem asks to determine at most d defective elements in a set of n elements, by queries to subsets that return Yes if the subset contains some defective, and No if the subset is free of defectives. By the entropy lower bound, $\log_2\sum_{i=0}^d{n\choose i}$ tests, which is essentially d log2 n , are needed at least. We devise group testing strategies that combine two features: They achieve this optimal query bound asymptotically, with a factor 1+o (1) as n grows, and they work in a fixed number of stages of parallel queries. Our strategies are randomized and have a controlled failure probability, i.e., constant but arbitrarily small. We consider different settings (known or unknown d , probably correct or verified outcome), and we aim at the smallest possible number of stages. In particular, 2 stages are sufficient if d grows slowly enough with n , and 4 stages are sufficient if d =o (n ).