# Circle Packing for Origami Design Is Hard

- Published in 2010
- Added on

In the collection

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 8/pi=2.546... These results are motivated by problems arising in the context of origami design.

## Links

## Other information

- journal
- Arxiv preprint arXiv:1008.1224
- pages
- 1--17
- publisher
- arxiv.org

### BibTeX entry

@article{Demaine2010, title = {Circle Packing for Origami Design Is Hard}, author = {Demaine, E.D. and Fekete, S.P. and Lang, R.J.}, url = {http://arxiv.org/abs/1008.1224 http://arxiv.org/pdf/1008.1224v2}, 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 8/pi=2.546... These results are motivated by problems arising in the context of origami design.}, journal = {Arxiv preprint arXiv:1008.1224}, pages = {1--17}, publisher = {arxiv.org}, year = 2010, urldate = {2010-08-13}, archivePrefix = {arXiv}, eprint = {1008.1224}, collections = {Geometry} }