Efficient (nonrandom) construction and decoding for non-adaptive group testing

The task of non-adaptive group testing is to identify up to d defective items from N items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are t tests, they can be represented as a t × N measurement matrix. We have answered the question of whether there exists a scheme such that a larger measurement matrix, built from a given t × N measurement matrix, can be used to identify up to d defective items in time O(tlog₂N). In the meantime, a t × N nonrandom measurement matrix with t = (Equation Presented) can be obtained to identify up to d defective items in time poly(t). This is much better than the best well-known bound, t = O (²log²₂N). For the special case d = 2, there exists an efficient nonrandom construction in which at most two defective items can be identified in time 4 log²₂N using t = 4 log²₂N tests. Numerical results show that our proposed scheme is more practical than existing ones, and experimental results confirm our theoretical analysis. In particular, up to 2⁷= 128 defective items can be identified in less than 16s even for N =2¹⁰⁰.