Monotone Paths in Geometric Triangulations

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 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.