When can you fold a map?

Computational Geometry: Theory and Applications

Volumn 29, Issue 1, 2004, Pages 23-46

  Arkin, Esther M ^a   Bender, Michael A ^a   Demaine, Erik D ^b   Demaine, Martin L ^b   Mitchell, Joseph S B ^a   Sethia, Saurabh ^a   Skiena, Steven S ^c  

^a Stony Brook University   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Oregon State University   (United States)

Author keywords

Computational origami; Crease patterns; Folding; NP hardness; Sheet metal bending; String matching

Indexed keywords

EID: 84867944165     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2004.03.012     Document Type: Article

References (28)

1. E.M. Arkin, S.P. Fekete, and J.S.B. Mitchell An algorithmic study of manufacturing paperclips and other folded structures Computational Geometry 25 2003 117 138
2. M. Bern, and B. Hayes The complexity of flat origami Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, Atlanta 1996 175 183
3. G. Calinescu, H. Karloff, M. Thorup, Manuscript, 2000
4. P. Crescenzi, D. Goldman, Ch. Papadimitriou, A. Piccolboni, and M. Yannakakis On the complexity of protein folding J. Comput. Biol. 5 3 1998
5. E.D. Demaine, M.L. Demaine, and J.S.B. Mitchell Folding flat silhouettes and wrapping polyhedral packages: New results in computational origami Computational Geometry 16 1 2000 3 21
6. E.D. Demaine, and J.S.B. Mitchell Reaching folded states of a rectangular piece of paper Proceedings of the 13th Canadian Conference on Computational Geometry, Waterloo, Canada 2001 73 75 http://compgeo.math.uwaterloo.ca/~cccg01/ proceedings/short/eddemaine-33029.ps
7. P. Di Francesco Folding and coloring problems in mathematics and physics Bull. Amer. Math. Soc. 37 3 2000 251 307
8. J. Edmonds, Personal communication, August 1997
9. M. Farach Optimal suffix tree construction with large alphabets Proceedings of the 38th Annual Symposium on Foundations of Computer Science, Miami Beach, FL 1997 137 143
10. M. Gardner The combinatorics of paper folding Wheels, Life and Other Mathematical Amusements 1983 Freeman 60 73
11. M.R. Garey, and D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness 1979 Freeman
12. D. Harel, and R. Endre Tarjan Fast algorithms for finding nearest common ancestors SIAM J. Comput. 13 2 1984 338 355
13. T. Hull On the mathematics of flat origamis Congressus Numerantium 100 1994 215 224
14. J. Justin Towards a mathematical theory of origami K. Miura, Proceedings of the 2nd International Meeting of Origami Science and Scientific Origami, Otsu, Japan 1994 15 29
15. R.M. Karp, and M.O. Rabin Efficient randomized pattern-matching algorithms IBM J. Res. Develop. 31 2 1987 249 260
16. T. Kawasaki On the relation between mountain-creases and valley-creases of a flat origami H. Huzita, Proceedings of the 1st International Meeting of Origami Science and Technology, Ferrara, Italy 1989 229 237 An unabridged Japanese version appeared in Sasebo College of Technology Report 27 1990 153 157
17. J.E. Koehler Folding a strip of stamps J. Combin. Theory 5 1968 135 152 Minor errata appear in Series A 19 3 1975 367
18. R.J. Lang A computational algorithm for origami design Proceedings of the 12th Annual ACM Symposium on Computational Geometry, Philadelphia, PA 1996 98 105
19. L. Lu, and S. Akella Folding cartons with fixtures: A motion planning approach IEEE Trans. Robotics Autom. 16 4 2000 346 356
20. W.F. Lunnon A map-folding problem Math. Comput. 22 101 1968 193 199
21. W.F. Lunnon Multi-dimensional map-folding Computer J. 14 1 1971 75 80
22. R. Motwani, and P. Raghavan Randomized Algorithms 1995 Cambridge University Press 213 221
23. B. Schieber, and U. Vishkin On finding lowest common ancestors: Simplification and parallelization SIAM J. Comput. 17 6 1988 1253 1262
24. J.S. Smith, Origami profiles, British Origami, 58, June 1976
25. J.S. Smith, Pureland Origami 1, 2 and 3, British Origami Society. Booklets 14, 29 and 43, 1980, 1988 and 1993
26. M. Thorup Faster deterministic sorting and priority queues in linear space Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA 1998 550 555
27. J. Touchard Contribution à l'étude du problème des timbres poste (Contribution to the study of the problem of postage stamps) Canadian J. Math. 2 1950 385 398
28. C.-H. Wang, Manufacturability-driven decomposition of sheet metal, PhD Thesis, Carnegie Mellon University, Robotics Institute, Technical Report CMU-RI-TR-97-35, September 1997