In this paper, we study the problem of computing a minimum-width double-strip or parallelogram annulus that encloses a given set of n points in the plane. A double-strip is a closed region in the plane whose boundary consists of four parallel lines and a parallelogram annulus is a closed region between two edge-parallel parallelograms. We present several first algorithms for these problems. Among them are $O(n^2)$ and $O(n^3\log n)$-time algorithms that compute a minimum-width double-strip and parallelogram annulus, respectively, when their orientations can be freely chosen.

中文翻译：

---

最小宽度的双条纹和平行四边形环

在本文中，我们研究了计算最小宽度的双条纹或平行四边形环面的问题，该环面将给定的n个点封装在平面中。双条带是平面中的闭合区域，其边界由四条平行线组成，平行四边形环是两个边缘平行平行四边形之间的闭合区域。针对这些问题，我们提出了几种优先算法。其中有$Ø（{ñ}^2）$ 和 $Ø（{ñ}^3\mathrm{日志}ñ）$时算法，当可以自由选择方向时，分别计算最小宽度的双带和平行四边形环。