dc.contributor.author | Schulz, André | |
dc.contributor.author | Demaine, Erik D | |
dc.date.accessioned | 2017-05-09T18:45:59Z | |
dc.date.available | 2018-01-07T06:00:05Z | |
dc.date.issued | 2017-03 | |
dc.identifier.issn | 0179-5376 | |
dc.identifier.issn | 1432-0444 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/108786 | |
dc.description.abstract | A stacking operation adds a d-simplex on top of a facet of a simplicial d-polytope while maintaining the convexity of the polytope. A stacked d-polytope is a polytope that is obtained from a d-simplex and a series of stacking operations. We show that for a fixed d every stacked d-polytope with n vertices can be realized with nonnegative integer coordinates. The coordinates are bounded by O(n[superscript 2 log[subscript 2](2d)], except for one axis, where the coordinates are bounded by O(n[superscript 3 log[subscript 2](2d)]. The described realization can be computed with an easy algorithm. The realization of the polytopes is obtained with a lifting technique which produces an embedding on a large grid. We establish a rounding scheme that places the vertices on a sparser grid, while maintaining the convexity of the embedding. | en_US |
dc.publisher | Springer US | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s00454-017-9887-6 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Springer US | en_US |
dc.title | Embedding Stacked Polytopes on a Polynomial-Size Grid | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Demaine, Erik D., and André Schulz. “Embedding Stacked Polytopes on a Polynomial-Size Grid.” Discrete & Computational Geometry 57, no. 4 (March 21, 2017): 782–809. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.mitauthor | Demaine, Erik D | |
dc.relation.journal | Discrete & Computational Geometry | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2017-04-25T03:46:25Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer Science+Business Media New York | |
dspace.orderedauthors | Demaine, Erik D.; Schulz, André | en_US |
dspace.embargo.terms | N | en |
dc.identifier.orcid | https://orcid.org/0000-0003-3803-5703 | |
mit.license | OPEN_ACCESS_POLICY | en_US |