Noise-resilient group testing: Limitations and constructions
Discrete Applied Mathematics
Testers and their applications
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 754.84 |
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 $\Theta\left({\min[r^2 \ln n,n]}\right)$ 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 $[m,k,\delta m]_q$ meeting the Gilbert-Varshamov bound may be constructed quite efficiently, in $\Theta\left({q^km}\right)$ time.