Lower Bound for Non-Adaptive Estimation of the Number of Defective Items

Abstract

We prove that to estimate within a constant factor the number of defective items in a non-adaptive randomized group testing algorithm we need at least Ω̃(logn) tests. This solves the open problem posed by Damaschke and Sheikh Muhammad in [6, 7]. 2012 ACM Subject Classification Mathematics of computing; Mathematics of computing→ Discrete mathematics; Mathematics of computing → Probabilistic algorithms; Theory of computation → Probabilistic computation