We are given positive integers $n$, $m$ and a set $S$ of subsets of the set $\{1,2,...,n\}$ with $|S| = m$.
For example:
$n = 5,\,\, m = 4,\,\, S = \{\, \{1,2\}, \{1,3\}, \{4,5\}, \{2,3\} \,\}.$
What is the fastest way to find the minimal subset $S'$ of $S$ such that the union of sets in $S'$ is equal to $\{1,2,...,n\}$.
In our example, there are 3 possible answers:
$S' = \{\,\{1,2\}, \{1,3\}, \{4,5\}\,\} \\ S' = \{\,\{1,2\}, \{2,3\}, \{4,5\}\,\} \\ S' = \{\,\{1,3\}, \{2,3\}, \{4,5\}\,\}$