Explicit Non-Adaptive Combinatorial Group Testing Schemes
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 $\bigT{\min[r^2 \ln n,n]}$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2007
- DOI:
- 10.48550/arXiv.0712.3876
- arXiv:
- arXiv:0712.3876
- Bibcode:
- 2007arXiv0712.3876P
- Keywords:
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- Computer Science - Data Structures and Algorithms
- E-Print:
- 15 pages, accepted to ICALP 2008