2026-07-24T18:54:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:2241 2024-03-06T11:08:52Z ddc:004 open_access

Explicit Non-Adaptive Combinatorial Group Testing Schemes Porat, Ely Rotschild, Amir Prime Numbers Group Testing Streaming Pattern Matching 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ely Porat and Amir Rotschild 2009 Is Part Of Dagstuhl Seminar Proceedings, Volume 9281, Search Methodologies (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.09281.2 urn:nbn:de:0030-drops-22414 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.2 eng https://creativecommons.org/licenses/by/4.0/legalcode