Minimal Product Set in Non-Abelian Metacyclic Groups of Even Order

Given a finite group $G$ and positive integers $r$ and $s$, a problem of interest in algebra is determining the minimum cardinality of the product set $AB$, where $A$ and $B$ are subsets of $G$ such that $|A|=r$ and $|B|=s$. This problem has been solved for the class of abelian groups; however, it r