Improved Non-Adaptive Algorithms for Threshold Group Testing With a Gap

The basic goal of threshold group testing is to identify up $d$ defective items among a population notation="LaTeX">$n$ items, where usually much smaller than . outcome test on subset positive if the has at least notation="LaTeX">$u$ negative it notation="LaTeX">$\ell $ notation="LaTeX">$0 \leq \ell < u$ , and arbitrary otherwise. This called testing. parameter notation="LaTeX">$g = u - 1$ the gap In this paper, we focus case > 0$ i.e., with gap. Note that results presented here are also applicable ; however, not as efficient those in related work. Currently, few reported studies have investigated designs decoding algorithms for identifying items. Most previous been feasible because there numerous constraints their problem settings or complexities proposed schemes relatively large. Therefore, compulsory reduce number tests well complexity, time achieving practical schemes. work makes five contributions. first more accurate theorem non-adaptive algorithm by Chen Fu. second an improvement construction disjunct matrices, which main tools tackling (threshold) other tasks such constructing cover-free families learning hidden graphs. Specifically, present better exact upper bound matrices compared third fourth contributions reduced asymptotic noisy setting outcomes. fifth contribution simulation resulting improvements theorems.