Embedding Ray Intersection Graphs and Global Curve Simplification

08/31/2021

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by   Mees van de Kerkhof, et al.

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We prove that circle graphs (intersection graphs of circle chords) can be embedded as intersection graphs of rays in the plane with polynomial-size bit complexity. We use this embedding to show that the global curve simplification problem for the directed Hausdorff distance is NP-hard. 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.