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Algorithmic enumeration of surrounding polygons
Discrete Applied Mathematics ( IF 1.0 ) Pub Date : 2020-04-01 , DOI: 10.1016/j.dam.2020.03.034
Katsuhisa Yamanaka , David Avis , Takashi Horiyama , Yoshio Okamoto , Ryuhei Uehara , Tanami Yamauchi

Abstract We are given a set S of points in the Euclidean plane. We assume that S is in general position. A simple polygon P is a surrounding polygon of S if each vertex of P is a point in S and every point in S is either inside P or a vertex of P . In this paper, we present an enumeration algorithm of the surrounding polygons for a given point set. Our algorithm is based on reverse search by Avis and Fukuda and enumerates all the surrounding polygons in polynomial delay and quadratic space. It also provides the first space efficient method to generate all simple polygonizations on a given point set in exponential time. By relating these two problems we provide an upper bound on the number of surrounding polygons.

中文翻译:

周围多边形的算法枚举

摘要 我们给定了欧几里得平面上的一组点。我们假设 S 处于一般位置。如果 P 的每个顶点都是 S 中的一个点并且 S 中的每个点都在 P 内部或 P 的顶点,则简单多边形 P 是 S 的周围多边形。在本文中,我们提出了一种给定点集周围多边形的枚举算法。我们的算法基于 Avis 和 Fukuda 的反向搜索,并在多项式延迟和二次空间中枚举所有周围的多边形。它还提供了第一个空间高效的方法,可以在指数时间内在给定的点集上生成所有简单的多边形化。通过将这两个问题联系起来,我们提供了周围多边形数量的上限。
更新日期:2020-04-01
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