Discrete Applied Mathematics - ARIDAM IV and V
Comparing File Copies with at Most Three Disagreeing Pages
IEEE Transactions on Computers
The Algorithmic Complexity of Chemical Threshold Testing
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Group Testing Problems with Sequences in Experimental Molecular Biology
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
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We consider a generalization of the classical group testing problem. Let us be given a sample contaminated with a chemical substance. We want to estimate the unknown concentration c of this substance in the sample. There is a threshold indicator which can detect whether the concentration is at least a known threshold. We consider either the case when the threshold indicator does not affect the tested units and the more difficult case when the threshold indicator destroys the tested units. For both cases, we present a family of efficient algorithms each of which achieves a good approximation of c using a small number of tests and of auxiliary resources. Each member of the family provides a different tradeoff between the number of tests and the use of other resources involved by the algorithm. Previously known algorithms for this problem use more tests than most of our algorithms do. For the case when the indicator destroys the tested units, we also describe a family of efficient algorithms which estimates c using only a constant number of tubes.