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arXiv · 1608.04812

Monotone Paths in Geometric Triangulations

Adrian Dumitrescu·Ritankar Mandal·Csaba D. Tóth
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Abstract

(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 $\Omega(1.7003^n)$. (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.

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Adrian Dumitrescu, Ritankar Mandal, Csaba D. Tóth. 2016-08-16. Monotone Paths in Geometric Triangulations. https://arxiv.org/abs/1608.04812

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