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dc.contributor.authorSchulz, André
dc.contributor.authorDemaine, Erik D
dc.date.accessioned2017-05-09T18:45:59Z
dc.date.available2018-01-07T06:00:05Z
dc.date.issued2017-03
dc.identifier.issn0179-5376
dc.identifier.issn1432-0444
dc.identifier.urihttp://hdl.handle.net/1721.1/108786
dc.description.abstractA 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.publisherSpringer USen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00454-017-9887-6en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceSpringer USen_US
dc.titleEmbedding Stacked Polytopes on a Polynomial-Size Griden_US
dc.typeArticleen_US
dc.identifier.citationDemaine, 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.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorDemaine, Erik D
dc.relation.journalDiscrete & Computational Geometryen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2017-04-25T03:46:25Z
dc.language.rfc3066en
dc.rights.holderSpringer Science+Business Media New York
dspace.orderedauthorsDemaine, Erik D.; Schulz, Andréen_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0003-3803-5703
mit.licenseOPEN_ACCESS_POLICYen_US


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