Circle Packing for Origami Design Is Hard
Computational Geometry
2010-09-21 v2 Computational Complexity
Discrete Mathematics
Abstract
We show that deciding whether a given set of circles can be packed into a rectangle, an equilateral triangle, or a unit square are NP-hard problems, settling the complexity of these natural packing problems. On the positive side, we show that any set of circles of total area 1 can be packed into a square of size 4/\sqrt{pi}=2.2567... These results are motivated by problems arising in the context of origami design.
Keywords
Cite
@article{arxiv.1008.1224,
title = {Circle Packing for Origami Design Is Hard},
author = {Erik D. Demaine and Sandor P. Fekete and Robert J. Lang},
journal= {arXiv preprint arXiv:1008.1224},
year = {2010}
}
Comments
17 pages, 13 figures. An abstract was presented at the 5th International Conference on Origami in Science, Mathematics and Education (5OSME). Updated to fix a numerical typo related to Figure 13, and a new result