Paper by Erik D. Demaine

Josh Brunner, Erik D. Demaine, Della Hendrickson, Victor Luo, and Andy Tockman, “Complexity of Simple Folding Orthogonal Crease Patterns”, in Abstracts from the 23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games (TJCDCGGG 2021), September 3–5, 2021, pages 26–27.

Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple folding problem — deciding which crease patterns can be folded flat by a sequence of (some model of) simple folds. We give new efficient algorithms for mixed crease patterns, where some creases are assigned mountain/valley while others are unassigned, for all 1D cases and for 2D rectangular paper with one-layer simple folds. By contrast, we show strong NP-completeness for mixed crease patterns on 2D rectangular paper with some-layers simple folds, complementing a previous result for all-layers simple folds. We also prove strong NP-completeness for finite simple folds (no matter the number of layers) of unassigned orthogonal crease patterns on arbitrary paper, complementing a previous result for assigned crease patterns, and contrasting with a previous positive result for infinite all-layers simple folds. In total, we obtain a characterization of polynomial vs. NP-hard for all cases — finite/infinite one/some/all-layers simple folds of assigned/unassigned/mixed orthogonal crease patterns on 1D/rectangular/arbitrary paper — except the unsolved case of infinite all-layers simple folds of assigned orthogonal crease patterns on arbitrary paper.

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Related papers:
MixedSimpleFolds_TJM (Complexity of Simple Folding of Mixed Orthogonal Crease Patterns)

See also other papers by Erik Demaine.
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Last updated May 28, 2024 by Erik Demaine.