Efficient segment folding is hard

Takashi Horiyama, Fabian Klute, Matias Korman, Irene Parada, Ryuhei Uehara, Katsuhisa Yamanaka

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We introduce a computational origami problem which we call the segment folding problem: given a set of n line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding might alter the relative position between the segments, and a segment could split into two. We show that it is NP-hard to determine whether n line segments can be folded in n simple folding operations.
Original languageEnglish
Article number101860
JournalComputational Geometry
Number of pages19
Publication statusPublished - 2022


  • Computational origami
  • NP-hardness
  • Simple folds
  • Segment folding


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