Computational Complexity of Stamp Folding

  • Ryuhei UeharaEmail author


In this chapter, we introduce two new notions of computational origami. The first one is “folding complexity”, which is introduced to measure the number of folding. When you are given an origami design, you consider it is hard when the number of folding is more than one hundred. On the other hand, you feel it is easy when you obtain it after less than 10 times of folding. This intuition is formalized as folding complexity. The second one is “crease width”. When you fold an origami model, if you have many paper layers at a crease, it is hard to fold them accurately. This intuition is formalized as crease width. We give some algorithmic results and hardness proofs about these new concepts.


  1. [Gar67]
    M. Gardner, Mathematical games. Sci. Am. 216(3), 124–125 (1967); 216(4), 118–120 (1967); 217(1), 115 (1967)Google Scholar
  2. [Gar08]
    M. Gardner, Origami, Eleusis, and the Soma Cube: Martin Gardner’s Mathematical Diversions (Cambridge University Press, The New Martin Gardner Mathematical Library, 2008)Google Scholar
  3. [GJ79]
    M.R. Garey, D.S. Johnson, Computers and Intractability – A Guide to the Theory of NP-Completeness. Freeman (1979)Google Scholar
  4. [LZ77]
    J. Ziv, A. Lempel, A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3), 337–343 (1977)MathSciNetCrossRefGoogle Scholar
  5. [LZ78]
    J. Ziv, A. Lempel, Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5), 530–536 (1978)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.JAISTIshikawaJapan

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