English

Counting the Number of Crossings in Geometric Graphs

Computational Geometry 2020-09-04 v2

Abstract

A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an O(n2logn)O(n^2 \log n) algorithm to compute the number of pairs of edges that cross in a geometric graph on nn points. For layered, and convex geometric graphs the algorithm takes O(n2)O(n^2) time.

Keywords

Cite

@article{arxiv.1904.11037,
  title  = {Counting the Number of Crossings in Geometric Graphs},
  author = {Frank Duque and Ruy Fabila-Monroy and César Hernández-Vélez and Carlos Hidalgo-Toscano},
  journal= {arXiv preprint arXiv:1904.11037},
  year   = {2020}
}