When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09281.2
URN: urn:nbn:de:0030-drops-22414
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2241/
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### 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:DagSemProc.09281.2,
author =	{Porat, Ely and Rotschild, Amir},
title =	{{Explicit Non-Adaptive Combinatorial Group Testing Schemes}},
booktitle =	{Search Methodologies},
pages =	{1--13},
series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
ISSN =	{1862-4405},
year =	{2009},
volume =	{9281},
editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
}