Folding a Paper Strip to Minimize Thickness

  • Erik D. Demaine
  • David Eppstein
  • Adam Hesterberg
  • Hiro Ito
  • Anna Lubiw
  • Ryuhei Uehara
  • Yushi Uno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)


In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a “flat folding” is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where “thicker” creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.


Vertical Segment Level Assignment Input Segment Paper Layer Orthogonal Graph 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • David Eppstein
    • 2
  • Adam Hesterberg
    • 3
  • Hiro Ito
    • 4
  • Anna Lubiw
    • 5
  • Ryuhei Uehara
    • 6
  • Yushi Uno
    • 7
  1. 1.Computer Science and Artificial Intelligence LabMassachusetts Institute of TechnologyUSA
  2. 2.Computer Science DepartmentUniversity of CaliforniaIrvineUSA
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyUSA
  4. 4.School of Informatics and EngineeringUniversity of Electro-CommunicationsJapan
  5. 5.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada
  6. 6.School of Information ScienceJapan Advanced Institute of Science and TechnologyJapan
  7. 7.Graduate School of ScienceOsaka Prefecture UniversityJapan

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