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URN: urn:nbn:de:0030-drops-22414
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2241/
Porat, Ely ; Rotschild, Amir

Explicit Non-Adaptive Combinatorial Group Testing Schemes

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Abstract

Group testing is a long studied problem in combinatorics: A small set of r ill people should be identified out of the whole (n people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we provide an explicit construction of a testing scheme which is better (smaller) than any known explicit construction. This scheme has \Theta(min[r2 log n, n])tests which is as many as the best non-explicit schemes have. In our construction we use a fact that may have a value by its own right: Linear error-correction codes with parameters [m, k, \delta m]q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in \Theta[q^{k}m) time.

BibTeX - Entry

@InProceedings{porat_et_al:DSP:2009:2241,
  author =	{Ely Porat and Amir Rotschild},
  title =	{Explicit Non-Adaptive Combinatorial Group Testing Schemes},
  booktitle =	{Search Methodologies },
  year =	{2009},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  number =	{09281},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2241},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}
}

Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching
Seminar: 09281 - Search Methodologies
Issue date: 2009
Date of publication: 10.11.2009

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