几何三角剖分中的单调路径
Monotone Paths in Geometric Triangulations
摘要：
(I)证明了平面上$n$点的几何三角剖分中单调路径的最大个数为$O(1.7864^n)$。这改进了早期的$O(1.8393^n)$上限;当前最佳下限是$Ω(1.7003^n)$。(II)给定一个平面几何图$G$，其顶点为$n$，证明了$G$中单调路的个数可以在$O(n^2)$时间内计算.
英文摘要：
(I) We prove that the (maximum) number of monotone paths in a geometric triangulation of $n$ points in the plane is $O(1.7864^n)$. This improves an earlier upper bound of $O(1.8393^n)$; the current best lower bound is $Ω(1.7003^n)$. (II) Given a planar geometric graph $G$ with $n$ vertices, we show that the number of monotone paths in $G$ can be computed in $O(n^2)$ time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
