Embedding Ray Intersection Graphs and Global Curve Simplification
Abstract
We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomialsize bit complexity. We use this embedding to show that the global curve simplification problem for the directed Hausdorff distance is NPhard. In this problem, we are given a polygonal curve $P$ and the goal is to find a second polygonal curve $P'$ such that the directed Hausdorff distance from $P'$ to $P$ is at most a given constant, and the complexity of $P'$ is as small as possible.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2109.00042
 Bibcode:
 2021arXiv210900042V
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 Appears in the Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021)