# Monotone Paths in Geometric Triangulations

Monotone Paths in Geometric Triangulations (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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

# Monotone Paths in Geometric Triangulations

, Volume 62 (6) – Feb 28, 2018
35 pages

/lp/springer_journal/monotone-paths-in-geometric-triangulations-OAIdnXo0nL
Publisher
Springer Journals
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
DOI
10.1007/s00224-018-9855-4
Publisher site
See Article on Publisher Site

### 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.

### Journal

Theory of Computing SystemsSpringer Journals

Published: Feb 28, 2018

### References

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