Explicit Non-Adaptive Combinatorial Group Testing Schemes

2007/12/22 by Porat, Ely, Rothschild, Amir
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.0712.3876

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 \bigTmin[r² ln 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,δm]_q meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in \bigTq^km time.

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