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 annulus 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.

环非正式地是一个环形区域，通常由两个同心圆描述。最大宽度的空环面问题要求找到具有最大可能宽度的某种形状的环面，该环面避免了平面中n个给定点的集合。这个问题也可以解释为在输入点之间找到环形有害设施的最佳位置的问题。在本文中，我们研究了最大宽度的空环问题的正方形和矩形变体，并提出了第一个非平凡算法。具体来说，我们的算法在$Ø（{ñ}^3）$ 和 $Ø（{ñ}^2\mathrm{日志}ñ）$计算最大宽度的空轴平行的正方形和矩形环的时间。两种算法都只使用$Ø（ñ）$ 空间。