Theory of Computing Systems

, Volume 62, Issue 6, pp 1490–1524 | Cite as

Monotone Paths in Geometric Triangulations

  • Adrian Dumitrescu
  • Ritankar Mandal
  • Csaba D. Tóth
Part of the following topical collections:
  1. Special Issue on Combinatorial Algorithms


(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(n2) time.


Monotone path Triangulation Counting algorithm 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Adrian Dumitrescu
    • 1
  • Ritankar Mandal
    • 1
  • Csaba D. Tóth
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of Wisconsin–MilwaukeeMilwaukeeUSA
  2. 2.Department of MathematicsCalifornia State UniversityNorthridge, Los AngelesUSA
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA

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