Explicit Non-Adaptive Combinatorial Group Testing Schemes

Porat, Ely; Rotschild, Amir

doi:10.4230/DagSemProc.09281.2

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Explicit Non-Adaptive Combinatorial Group Testing Schemes

Authors Ely Porat, Amir Rotschild

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 9281
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2009-11-10

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DOI: 10.4230/DagSemProc.09281.2
URN: urn:nbn:de:0030-drops-22414

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Keywords

Prime Numbers
Group Testing
Streaming
Pattern Matching

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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.

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Ely Porat and Amir Rotschild. Explicit Non-Adaptive Combinatorial Group Testing Schemes. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/DagSemProc.09281.2

Author Details

Ely Porat

Amir Rotschild

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