Folding a Paper Strip to Minimize Thickness
Name
1411.6371.pdf
Description
Submitted version
Size
170 KB
Format
Adobe PDF
Checksum (MD5)
6e2d5a8b64a76ed06a8486bb8b419685
Author(s)
Demaine, Erik D
Eppstein, David
Hesterberg, Adam
Ito, Hiro
Lubiw, Anna
Uehara, Ryuhei
Uno, Yushi
Date Issued
January 2016
Journal
Journal of Discrete Algorithms
Publisher
Springer Nature America, Inc
Citation
Demaine, Erik D., David Eppstein, Adam Hesterberg, Hiro Ito, Anna Lubiw, Ryuhei Uehara and Yushi Uno. "Folding a Paper Strip to Minimize Thickness." Journal of Discrete Algorithms 36: 18-26, 2016.
Version
Original manuscript
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 twometrics:minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close toflat), andminimizing 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 the first problem fixed-parameter tractable in 1D with respect to the number of layers.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-319-15612-5_11
