  An annulus is, informally, a ring-shaped region, often described by two
concentric circles. The maximum-width empty annulus problem asks to find an
annulus of a certain shape with the maximum possible width that avoids a given
set of $n$ points in the plane. This problem can also be interpreted as the
problem of finding an optimal location of a ring-shaped obnoxious facility
among the input points. In this paper, we study square and rectangular variants
of the maximum-width empty anuulus problem, and present first nontrivial
algorithms. Specifically, our algorithms run in $O(n^3)$ and $O(n^2 \log n)$
time for computing a maximum-width empty axis-parallel square and rectangular
annulus, respectively. Both algorithms use only $O(n)$ space.
