TY - JOUR
T1 - Explicit nonadaptive combinatorial group testing schemes
AU - Porat, Ely
AU - Rothschild, Amir
N1 - 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: [email protected]) Communicated by E. Arikan, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2011.2163296
PY - 2011/12
Y1 - 2011/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=83255193460&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2163296
DO - 10.1109/TIT.2011.2163296
M3 - مقالة
SN - 0018-9448
VL - 57
SP - 7982
EP - 7989
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 12
M1 - 5967914
ER -