Improved Algorithms for Chemical Threshold Testing Problems

  • Annalisa De Bonis
  • Luisa Gargano
  • Ugo Vaccaro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


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.


Concentration Ratio Group Testing Improve Algorithm Unknown Concentration Logarithmic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    E. Barillot et al., “Theoretical analysis of library screening using a n-dimensional pooling strategy”, Nucleic Acids Research, (1991), 6241–6247.Google Scholar
  2. 2.
    J.L. Bentley and A. Yao, “An almost optimal algorithm for unbounded search”, IPL 5, (1976), 82–87.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    W. J. Bruno et al., “Design of efficient pooling experiments”, Genomics, vol., 26, (1995), 21–30.CrossRefGoogle Scholar
  4. 4.
    P. Damaschke, “The algorithmic complexity of chemical threshold testing”, in: CIAC’ 97, LNCS, 1203, Springer-Verlag, (1997), 215–216.Google Scholar
  5. 5.
    R. Dorfman, “The detection of defective members of large populations”, Ann. Math. Stat., 14 (1943), 436–440.CrossRefGoogle Scholar
  6. 6.
    D.Z. Du and F.K. Hwang, “Competitive group testing”, Discrete Applied Math., 45 (1993), 221–232.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    D.Z. Du and F.K. Hwang, Combinatorial Group Testing and its Applications, World Scientific Publishing, (1993).Google Scholar
  8. 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
  9. 9.
    F.K. Hwang and P.J. Wan, “Comparing file copies with at most three disagreeing pages” IEEE Transactions on Computers, 46, No. 6, (June 1997), 716–718.CrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Sobel and P.A. Groll, “Group testing to eliminate efficiently all defectives in a binomial sample”, Bell System Tech. J. 38, (1959), 1179–1252.MathSciNetGoogle Scholar
  11. 11.
    J. K. Wolf, “Born again group testing: Multiacces communications”, IEEE Trans. Inf. Th. IT-31, (1985), 185–191.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Annalisa De Bonis
    • 1
  • Luisa Gargano
    • 1
  • Ugo Vaccaro
    • 1
  1. 1.Dipartimento di Informatica e ApplicazioniUniversità di SalernoBaronissi (SA)Italy

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