Algorithmic folding complexity
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Demaine_Algorithmic folding.pdf
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Author(s)
Cardinal, Jean
Demaine, Erik D.
Demaine, Martin L.
Imahori, Shinji
Langerman, Stefan
Uehara, Ryuhei
Date Issued
2009
Journal
Algorithms and computation : ... International Symposium, ISAAC ... : proceedings.
Publisher
Springer
Citation
Cardinal, Jean et al. “Algorithmic Folding Complexity.” Algorithms and Computation. Springer Berlin / Heidelberg, 2009. 452-461. (Lecture notes in computer science, v. 5878.)
Copyright © 2009, Springer
Version
Author's final manuscript
Abstract
How do we most quickly fold a paper strip (modeled as a line) to obtain a desired mountain-valley pattern of equidistant creases (viewed as a binary string)? Define the folding complexity of a mountain-valley string as the minimum number of simple folds required to construct it. We show that the folding complexity of a length-n uniform string (all mountains or all valleys), and hence of a length-n pleat (alternating mountain/valley), is polylogarithmic in n. We also show that the maximum possible folding complexity of any string of length n is O(n/lgn), meeting a previously known lower bound.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-642-10631-6_47
