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
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
Competitive group testing and learning hidden vertex covers with minimum adaptivity
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
New and improved BIST diagnosis methods from combinatorial Group testing theory
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Randomized group testing both query-optimal and minimal adaptive
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Synthetic sequence design for signal location search
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
An efficient FPRAS type group testing procedure to approximate the number of defectives
Journal of Combinatorial Optimization
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The classical and well-studied group testing problem is to find d defectives in a set of n elements by group tests, which tell us for any chosen subset whether it contains defectives or not. Strategies are preferred that use both a small number of tests close to the informationtheoretic lower bound d log n, and a small constant number of stages, where tests in every stage are done in parallel, in order to save time. They should even work if d is completely unknown in advance. An essential ingredient of such competitive and minimal-adaptive group testing strategies is an estimate of d within a constant factor. More precisely, d shall be underestimated only with some given error probability, and overestimated only by a constant factor, called the competitive ratio. The latter problem is also interesting in its own right. It can be solved with O(log n) randomized group tests of a certain type. In this paper we prove that Ω(log n) tests are really needed. The proof is based on an analysis of the influence of tests on the searcher's ability to distinguish between any two candidate numbers with a constant ratio. Once we know this lower bound, the next challenge is to get optimal constant factors in the O(log n) test number, depending on the desired error probability and competitive ratio. We give a method to derive upper bounds and conjecture that our particular strategy is already optimal.