Monotone Paths in Geometric Triangulations

  • Adrian Dumitrescu
  • Ritankar Mandal
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)

Abstract

(I) We prove that the (maximum) number of monotone paths in a triangulation of n points in the plane is \(O(1.8027^n)\). This improves an earlier upper bound of \(O(1.8393^n)\); the current best lower bound is \(\varOmega (1.7034^n)\). (II) Given a planar straight-line graph G with n vertices, we show that the number of monotone paths in G can be computed in \(O(n^2)\) time.

Keywords

Monotone path Triangulation Counting algorithm 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Adrian Dumitrescu
    • 1
  • Ritankar Mandal
    • 1
  • Csaba D. Tóth
    • 2
    • 3
  1. 1.University of Wisconsin-MilwaukeeMilwaukeeUSA
  2. 2.California State University NorthridgeLos AngelesUSA
  3. 3.Tufts UniversityMedfordUSA

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