Realization of abstract convex geometries by point configurations, Part 1
Kira Adaricheva, Marcel Wild
TL;DR
This paper investigates the problem of representing abstract convex geometries with point configurations in the plane, revealing that a natural modification relates to an NP-hard problem in order types.
Contribution
It establishes a connection between a modified Edelman-Jamison problem and the NP-hard order type problem, advancing understanding of geometric representations.
Findings
Modified Edelman-Jamison problem is NP-hard
Characterization of convex geometries in planar point sets
Link between convex geometry representation and computational complexity
Abstract
The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to the well known NP-hard order type problem.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Computational Geometry and Mesh Generation · Manufacturing Process and Optimization