Paper by Erik D. Demaine

Jean Cardinal, Erik D. Demaine, Martin L. Demaine, Shinji Imahori, Stefan Langerman, and Ryuhei Uehara, “Algorithmic Folding Complexity”, in Abstracts from the 7th Japan Conference on Computational Geometry and Graphs (JCCGG 2009), Kanazawa, Ishikawa, Japan, November 11–13, 2009, to appear.

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/lg n), meeting a previously known lower bound.

The paper is 2 pages.

The paper is available in PDF (372k).
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Related papers:
PleatFolding_GC (Algorithmic Folding Complexity)
PleatFolding_ISAAC2009 (Algorithmic Folding Complexity)

See also other papers by Erik Demaine.
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Last updated June 13, 2024 by Erik Demaine.