Simple set cardinality estimation through random sampling

Abstract

We present a simple algorithm that estimates the cardinality $n$ of a set $V$ when allowed to sample elements of $V$ uniformly and independently at random. Our algorithm with probability $(1-\delta)$ returns a $(1\pm\epsilon)-$approximation of $n$ drawing $O\big(\sqrt{n} \cdot \epsilon^{-1}\sqrt{\log(\delta^{-1})}\big)$ samples (for $\epsilon^{-1}\sqrt{\log(\delta^{-1})} = O(\sqrt{n})$).