• Corpus ID: 215786558

# Framework for $\exists \mathbb{R}$-Completeness of Two-Dimensional Packing Problems

@article{Abrahamsen2020FrameworkF,
title={Framework for \$\exists \mathbb\{R\}\$-Completeness of Two-Dimensional Packing Problems},
author={Mikkel Abrahamsen and Tillmann Miltzow and Nadja Seiferth},
journal={arXiv: Computational Geometry},
year={2020}
}
• Published 16 April 2020
• Mathematics
• arXiv: Computational Geometry
We show that many natural two-dimensional packing problems are algorithmically equivalent to finding real roots of multivariate polynomials. A two-dimensional packing problem is defined by the type of pieces, containers, and motions that are allowed. The aim is to decide if a given set of pieces can be placed inside a given container. The pieces must be placed so that they are pairwise interior-disjoint, and only motions of the allowed type can be used to move them there. We establish a…

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