DagSemProc.09281.2.pdf
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Explicit Non-Adaptive Combinatorial Group Testing Schemes
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Dagstuhl Seminar Proceedings, Volume 9281
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2009-11-10
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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
https://doi.org/10.4230/DagSemProc.09281.2
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.
Keywords
- Prime Numbers
- Group Testing
- Streaming
- Pattern Matching
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