• Corpus ID: 215786558

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

  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},
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… 



Covering Polygons is Even Harder

  • Mikkel Abrahamsen
  • Mathematics, Computer Science
    2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
  • 2022
It is proved that assuming the widespread belief that NP-hard MCC is not in N P, and the problem is thus $\exists \mathbb{R}$-complete, that many natural approaches to finding small covers are bound to give suboptimal solutions in some cases.

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