Journal of Combinatorial Optimization

, Volume 15, Issue 1, pp 49–59 | Cite as

A survey on nonadaptive group testing algorithms through the angle of decoding

  • Hong-Bin ChenEmail author
  • Frank K. Hwang


Group testing, sometimes called pooling design, has been applied to a variety of problems such as blood testing, multiple access communication, coding theory, among others. Recently, screening experiments in molecular biology has become the most important application. In this paper, we review several models in this application by focusing on decoding, namely, giving a comparative study of how the problem is solved in each of these models.


Group testing Pooling designs Nonadaptive algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alon N, Beigel R, Kasif S, Rudich S, Sudakov B (2004) Learning a hidden matching. SIAM J Comput 33:487–501 zbMATHCrossRefMathSciNetGoogle Scholar
  2. Balding DJ, Bruno WJ, Knill E, Torney DC (1996) A comparative survey of nonadaptive pooling designs. In: Genetic mapping and DNA sequencing. IMA volumes in mathematics and its applications. Springer, Berlin, pp 133–154 Google Scholar
  3. Chang FH, Chang HL, Hwang FK (2007) Pooling designs for clone library screening in the inhibitor complex model, to appear Google Scholar
  4. Chen HB, Du DZ, Hwang FK (2007) An unexpected meeting of four seemingly unrelated problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. J Comb Opt, to appear Google Scholar
  5. Chen HB, Fu HL, Hwang FK (2007) An upper bound of the number of tests in pooling designs for the error-tolerant complex model. Opt Lett, to appear Google Scholar
  6. De Bonis A, Vaccaro U (1998) Improved algorithms for group testing with inhibitors. Inform Process Lett 67:57–64 CrossRefMathSciNetGoogle Scholar
  7. De Bonis A, Vaccaro U (2003) Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels. Theor Comput Sci 306:223– 243 zbMATHCrossRefGoogle Scholar
  8. De Bonis A, Gasieniec L, Vaccaro U (2005) Optimal two-stage algorithms for group testing problems. SIAM J Comput 34:1253–1270 zbMATHCrossRefMathSciNetGoogle Scholar
  9. Du DZ, Hwang FK (2000) Combinatorial group testing and its applications, 2nd ed. World Scientific, Singapore zbMATHGoogle Scholar
  10. D’yachkov AG, Rykov VV (1983) A survey of superimposed code theory. Probl Control Inf Theory 12:229–242 MathSciNetGoogle Scholar
  11. D’yachkov AG, Macula AJ, Torney DC, Vilenkin PA (2001) Two models of nonadaptive group testing for designing screening experiments. In: Attkinson AC, Hackl P, Muller WG (eds) Proceedings of the 6th international workshop in model oriented design and analysis. Physica, Berlin, pp 63–75 Google Scholar
  12. D’yachkov AG, Vilenkin PA, Macula AJ, Torney DC (2002) Families of finite sets in which no intersection of sets is covered by the union of s others. J Comb Theory Ser A 99:195–218 zbMATHCrossRefMathSciNetGoogle Scholar
  13. Farach M, Kannan S, Knill E, Muthukrishnan S (1997) Group testing problem with sequences in experimental molecular biology. In: Proceedings of the compression and complexity of sequences, pp 357–367 Google Scholar
  14. Hwang FK, Liu YC (2003) Error-tolerant pooling designs with inhibitors. J Comput Biol 10:231–236 CrossRefGoogle Scholar
  15. Kim HK, Lebedev V (2004) On optimal superimposed codes. J Comb Des 12:79–91 zbMATHCrossRefMathSciNetGoogle Scholar
  16. Macula AJ, Popyack LJ (2004) A group testing method for finding patterns in data. Discret Appl Math 144:149–157 zbMATHCrossRefMathSciNetGoogle Scholar
  17. Mitchell CJ, Piper FC (1988) Key storage in secure networks. Discret Appl Math 21:215–228 zbMATHCrossRefMathSciNetGoogle Scholar
  18. Ngo HQ, Du DZ (2000) A survey on combinatorial group testing algorithms with applications to DNA library screening. In: DIMACS Ser Discret Math Theor Comput Sci, vol 55,. American Mathematical Society, Providence, pp 171–182 Google Scholar
  19. Stinson DR, Wei R (2004) Generalized cover-free families. Discret Math 279:463–477 zbMATHCrossRefMathSciNetGoogle Scholar
  20. Stinson DR, Wei R, Zhu L (2000) Some new bounds for cover-free families. J Comb Theory Ser A 90:224–234 zbMATHCrossRefMathSciNetGoogle Scholar
  21. Torney DC (1999) Sets pooling designs. Ann Comb 3:95–101 zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan

Personalised recommendations