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][1] by Paul Erdös and Sherman Stein <i>(Sums of distinct unit fractions. Proceedings of the American Mathematical Society, 14(1), 126-131, 1963.)</i> . Let $m(p,q)$ denote the minimal cardinality of such a subset $S$. Is there a polynomial-time algorithm to determine $m(p,q)$?

  [1]: https://www.renyi.hu/~p_erdos/1963-18.pdf