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Finding a Largest-Area Triangle in a Terrain in Near-Linear Time
arXiv - CS - Computational Geometry Pub Date : 2021-04-23 , DOI: arxiv-2104.11420
Sergio Cabello, Arun Kumar Das, Sandip Das, Joydeep Mukherjee

A terrain is an $x$-monotone polygon whose lower boundary is a single line segment. We present an algorithm to find in a terrain a triangle of largest area in $O(n \log n)$ time, where $n$ is the number of vertices defining the terrain. The best previous algorithm for this problem has a running time of $O(n^2)$.

中文翻译:

在近线性时间内在地形中找到最大面积的三角形

地形是$ x $单调多边形,其下边界是单个线段。我们提出一种算法,以在地形中找到在$ O(n \ log n)$时间内面积最大的三角形,其中$ n $是定义地形的顶点数量。以前针对该问题的最佳算法的运行时间为$ O(n ^ 2)$。
更新日期:2021-04-26
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