Monotone Paths in Geometric Triangulations

被引：0
|
作者：
Adrian Dumitrescu
Ritankar Mandal
Csaba D. Tóth
机构：
[1] University of Wisconsin–Milwaukee,Department of Computer Science
[2] California State University,Department of Mathematics
[3] Tufts University,Department of Computer Science
来源：
Theory of Computing Systems | 2018年 / 62卷
关键词：
Monotone path; Triangulation; Counting algorithm;
D O I：
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学科分类号：
摘要：
(I) We prove that the (maximum) number of monotone paths in a geometric triangulation of n points in the plane is O(1.7864n). This improves an earlier upper bound of O(1.8393n); the current best lower bound is Ω(1.7003n). (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(n2) time.
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页码：1490 / 1524
页数：34
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