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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/15056

Title: Folding a Paper Strip to Minimize Thickness
Authors: Demaine, Erik D.
Eppstein, David
Hesterberg, Adam
Ito, Hiro
Lubiw, Anna
Uehara, Ryuhei
Uno, Yushi
Keywords: linkage
NP-complete
optimization problem
rigid origami
Issue Date: 2015-10-28
Publisher: Elsevier
Magazine name: Journal of Discrete Algorithms
Volume: 36
Start page: 18
End page: 26
DOI: 10.1016/j.jda.2015.09.003
Abstract: In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a ``flat folding'' is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where ``thicker'' creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove both problems fixed-parameter tractable in 1D with respect to the number of layers.
Rights: Copyright (C)2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Erik D. Demaine, David Eppstein, Adam Hesterberg, Hiro Ito, Anna Lubiw, Ryuhei Uehara, and Yushi Uno, Journal of Discrete Algorithms, 36, 2015, 18-26, http://dx.doi.org/10.1016/j.jda.2015.09.003
URI: http://hdl.handle.net/10119/15056
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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