Packing identical simple polygons is NP-hard
Computational Geometry
2012-09-25 v1
Abstract
Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is presented where a small polygon is constructed to encode the entire circuit.
Cite
@article{arxiv.1209.5307,
title = {Packing identical simple polygons is NP-hard},
author = {Sarah R. Allen and John Iacono},
journal= {arXiv preprint arXiv:1209.5307},
year = {2012}
}