For any positive $p,q\in\mathbb{N}$ there is a finite subset $S$ of $\{\frac{1}{n}:n\in\mathbb{N}, n\geq 1\}$ such that $\sum_{s\in S} s=\frac{p}{q}$, see this article by Paul Erdös and Sherman Stein (Sums of distinct unit fractions. Proceedings of the American Mathematical Society, 14(1), 126-131, 1963.) . Let $m(p,q)$ denote the minimal cardinality of such a subset $S$. Is there a polynomial-time algorithm to determine $m(p,q)$?