Algorithmic Folding Complexity

Authors:
Jean Cardinal;Erik D. Demaine;Martin L. Demaine;Shinji Imahori;Stefan Langerman;Ryuhei Uehara
Affiliations:
Université Libre de Bruxelles (ULB), Brussels, Belgium B-1050;MIT, Cambridge, USA MA 02139;MIT, Cambridge, USA MA 02139;University of Tokyo, Tokyo, Japan 113-8656;Université Libre de Bruxelles (ULB), Brussels, Belgium B-1050;Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan 923-1292
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

Citing 2
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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 $O(n/\lg n)$, meeting a previously known lower bound.