Explicit nonadaptive combinatorial group testing schemes

Ely Porat, Amir Rothschild

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68 Scopus citations

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 Θ (min[r2 ln n,n]) tests which is as many as the best nonexplicit 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,δm]q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in Θ(qk m) time.

Original languageEnglish
Article number5967914
Pages (from-to)7982-7989
Number of pages8
JournalIEEE Transactions on Information Theory
Volume57
Issue number12
DOIs
StatePublished - Dec 2011

Bibliographical note

Funding Information:
Manuscript received October 04, 2010; revised April 03, 2011; accepted June 21, 2011. Date of publication August 01, 2011; date of current version December 07, 2011. This work was supported in part by BSF Grant 2006334 and in part by ISF Grant 1484/08. The authors are with Bar-Ilan University, Ramat Gan, Israel (e-mail: amirrot@gmail.com) Communicated by E. Arikan, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2011.2163296

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