I have two sets of points, $X$ and $Y$, which are finite and disjoint. I want to compute the distance between them defined by: $$d(X,Y)= \frac{\sum_{x \in X} \|x-Y\| + \sum_{y \in Y} \|y-X\|}{|x|+|y|} $$ where $\|x-Y\|$ represents the distance between the point $x$ in $X$ to its closest point in $Y$, and $|x|$, $|y|$ are the cardinalities of $X$ and $Y$ respectively.

Since both sets are large, the above formula is computationally expensive. How can I calculate it or bound it efficiently?