Area-Optimal Simple Polygonalizations: The CG Challenge 2019
Erik D. Demaine, S\'andor P. Fekete, Phillip Keldenich and, Dominik Krupke, Joseph S. B. Mitchell
TL;DR
This paper reviews the theoretical and practical challenges of finding area-optimal simple polygonalizations of point sets, highlighting the NP-hardness and the extensive challenge posed by the 2019 CG Challenge with large instances.
Contribution
It provides an overview of the NP-hard problems of Min-Area and Max-Area polygonalizations and discusses solutions from the 2019 CG Challenge for large-scale instances.
Findings
NP-hardness of Min-Area and Max-Area problems
Successful solutions for instances up to 1,000,000 points
Insights into practical approaches for large-scale polygonalizations
Abstract
We give an overview of theoretical and practical aspects of finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the plane. Both problems are known to be NP-hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging from n = 10 all the way to n = 1, 000, 000.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Constraint Satisfaction and Optimization · 3D Modeling in Geospatial Applications