# Explicit Non-Adaptive Combinatorial Group Testing Schemes - Computer Science > Data Structures and Algorithms

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 onlyqueries tests of the form -Does set X contain an ill human?-. In this paperwe provide an explicit construction of a testing scheme which is bettersmaller than any known explicit construction. This scheme has $\bigT{\minr^2\ln n,n}$ tests which is as many as the best non-explicit schemes have. In ourconstruction we use a fact that may have a value by its own right: Linearerror-correction codes with parameters $m,k,\delta m q$ meeting theGilbert-Varshamov bound may be constructed quite efficiently, in $\bigT{q^km}$time.

Author: Ely Porat, Amir Rothschild

Source: https://arxiv.org/