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.
@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}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.2}, URN = {urn:nbn:de:0030-drops-22414}, doi = {10.4230/DagSemProc.09281.2}, annote = {Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching} }
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