We prove that to estimate within a constant factor the number of defective items in a non-adaptive group testing algorithm we need at least $\tilde\Omega((\log n)(\log(1/\delta)))$ tests. This solves the open problem posed by Damaschke and Sheikh Muhammad.

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Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$ contains at least ... more >>>

We consider the following problem: Given an $n \times n$ multiplication table, decide whether it is a Cayley multiplication table of a group. Among deterministic algorithms for this problem, the best known algorithm is implied by F. W. Light's associativity test (1949) and has running time of $O(n^2 \log n)$. ... more >>>