Framework for ER-Completeness of Two-Dimensional Packing Problems

@article{Abrahamsen2020FrameworkFE,
  title={Framework for ER-Completeness of Two-Dimensional Packing Problems},
  author={Mikkel Abrahamsen and Tillmann Miltzow and Nadja Seiferth},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2020},
  pages={1014-1021}
}
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 in the resulting placement, they are pairwise interior-disjoint, and only motions of the allowed type can be used to move them… 

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