  Given two point sets in the plane, we study the minimization of the
bottleneck distance between a point set B and an equally-sized subset of a
point set A under translations. We relate this problem to a Voronoi-type
diagram and derive polynomial bounds for its complexity that are optimal in the
size of A. We devise efficient algorithms for the construction of such a
diagram and its lexicographic variant, which generalize to higher dimensions.
We use the diagram to find an optimal bottleneck matching under translations,
to compute a connecting path of minimum bottleneck cost between two positions
of B, and to determine the maximum bottleneck cost in a convex polygon.
