Explicit Non-Adaptive Combinatorial Group Testing Schemes

Details Explicit Non-Adaptive Combinatorial Group Testing Schemes Explicit Non-Adaptive Combinatorial Group Testing Schemes

2007-12-22

arxiv.org/abs/0712.3876v5

Computer Science

Data Structures and Algorithms

15 pages, accepted to ICALP 2008

Scientific paper

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 $\bigT{\min[r^2 \ln n,n]}$ 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 $[m,k,\delta m]_q$ meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in $\bigT{q^km}$ time.

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