@article{oai:ipsj.ixsq.nii.ac.jp:00208822,
 author = {Erik, D. Demaine and Martin, L. Demaine and Hiro, Ito and Chie, Nara and Izumi, Shirahama and Tomohiro, Tachi and Mizuho, Tomura and Erik, D. Demaine and Martin, L. Demaine and Hiro, Ito and Chie, Nara and Izumi, Shirahama and Tomohiro, Tachi and Mizuho, Tomura},
 issue = {12},
 journal = {情報処理学会論文誌},
 month = {Dec},
 note = {Deciding flat foldability of a given mountain-valley pattern is known to be NP-complete. One special case known to be solvable in linear time is when the creases are parallel to each other and perpendicular to two sides of a rectangular piece of paper; this case reduces to a purely one-dimensional folding problem. In this paper, we give linear-time algorithms for flat foldability in two more-general special cases: (1) all creases are parallel to each other and to two sides of a parallelogram of paper, but possibly oblique to the other two sides of the parallelogram; and (2) creases form a regular zigzag whose two directions (zig and zag, again possibly oblique to the two sides of the piece of paper) form nonacute angles to each other. In the latter zigzag case, we in fact prove that every crease pattern can be folded flat, even if each crease is specified as mountain, valley, or unfolded.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.28(2020) (online)
DOI　http://dx.doi.org/10.2197/ipsjjip.28.825
------------------------------, Deciding flat foldability of a given mountain-valley pattern is known to be NP-complete. One special case known to be solvable in linear time is when the creases are parallel to each other and perpendicular to two sides of a rectangular piece of paper; this case reduces to a purely one-dimensional folding problem. In this paper, we give linear-time algorithms for flat foldability in two more-general special cases: (1) all creases are parallel to each other and to two sides of a parallelogram of paper, but possibly oblique to the other two sides of the parallelogram; and (2) creases form a regular zigzag whose two directions (zig and zag, again possibly oblique to the two sides of the piece of paper) form nonacute angles to each other. In the latter zigzag case, we in fact prove that every crease pattern can be folded flat, even if each crease is specified as mountain, valley, or unfolded.
------------------------------
This is a preprint of an article intended for publication Journal of
Information Processing(JIP). This preprint should not be cited. This
article should be cited as: Journal of Information Processing Vol.28(2020) (online)
DOI　http://dx.doi.org/10.2197/ipsjjip.28.825
------------------------------},
 title = {Flat Folding a Strip with Parallel or Nonacute Zigzag Creases with Mountain-Valley Assignment},
 volume = {61},
 year = {2020}
}