Improved Algorithms for Chemical Threshold Testing Problems
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.
KeywordsConcentration Ratio Group Testing Improve Algorithm Unknown Concentration Logarithmic Number
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- 1.E. Barillot et al., “Theoretical analysis of library screening using a n-dimensional pooling strategy”, Nucleic Acids Research, (1991), 6241–6247.Google Scholar
- 4.P. Damaschke, “The algorithmic complexity of chemical threshold testing”, in: CIAC’ 97, LNCS, 1203, Springer-Verlag, (1997), 215–216.Google Scholar
- 7.D.Z. Du and F.K. Hwang, Combinatorial Group Testing and its Applications, World Scientific Publishing, (1993).Google Scholar
- 8.M. Farach et al., “Group testing problems with sequences in experimental molecular biology”, in: Proc. Compr. and Compl. of Sequences’ 97, B. Carpentieri, A. De Santis, J. Storer, and U. Vaccaro, (Eds.), IEEE Computer Society, pp. 357–367.Google Scholar