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.
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Cardinal, J., Demaine, E.D., Demaine, M.L., Imahori, S., Langerman, S., Uehara, R. (2009). Algorithmic Folding Complexity. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_47
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DOI: https://doi.org/10.1007/978-3-642-10631-6_47
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