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No Easy Puzzles: A Hardness Result for Jigsaw Puzzles

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Fun with Algorithms (FUN 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8496))

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Abstract

We show that solving jigsaw puzzles requires Θ(n 2) edge matching comparisons, making them as hard as their trivial upper bound. This result generalises to puzzles of all shapes, and is applicable to both pictorial and apictorial puzzles.

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References

  1. Norgate, M.: Cutting borders: Dissected maps and the origins of the jigsaw puzzle. Cartogr. J. 44(4), 342–350 (2007)

    Article  Google Scholar 

  2. Yao, F.H., Shao, G.F.: A shape and image merging technique to solve jigsaw puzzles. Pattern Recogn. Lett. 24, 1819–1835 (2003)

    Article  Google Scholar 

  3. Freeman, H., Garder, L.: Apictorial jigsaw puzzles: The computer solution of a problem in pattern recognition. IEEE Trans. Electron. Comput. EC-13, 118–127 (1964)

    Google Scholar 

  4. Kleber, F., Sablatnig, R.: Scientific puzzle solving: current techniques and applications. In: Computer Applications to Archaeology (CAA 2009), Williamsburg, Virginia (March 2009)

    Google Scholar 

  5. Kong, W., Kimia, B.B.: On solving 2D and 3D puzzles using curve matching. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, Hawaii (December 2001)

    Google Scholar 

  6. Radack, G.M., Badler, N.I.: Jigsaw puzzle matching using a boundary-centered polar encoding. Comput. Vision Graph. 19, 1–17 (1982)

    Google Scholar 

  7. Webster, R.W., Ross, P.W., Lafollette, P.S., Stafford, R.L.: A computer vision system that assembles canonical jigsaw puzzles using the euclidean skeleton and Isthmus critical points. In: IAPR Workshop on Machine Vision Applications (MVA 1990), Tokyo, IAPR, pp. 118–127 (November 1990)

    Google Scholar 

  8. Gallagher, A.C.: Jigsaw puzzles with pieces of unknown orientation. In: 25th Conf. Computer Vision and Pattern Recognition (CVPR 2012), Providence, Rhode Island (June 2012)

    Google Scholar 

  9. Sağıroğlu, M.Ş., Erçil, A.: Optimization for automated assembly of puzzles. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research 18(2), 321–338 (2010)

    Article  MATH  Google Scholar 

  10. Wolfson, H., Schonberg, E., Kalvin, A., Lamdan, Y.: Solving jigsaw puzzles by computer. Ann. Oper. Res. 12(1-4), 51–64 (1988)

    Article  MathSciNet  Google Scholar 

  11. Arvind, V., Köbler, J.: Graph isomorphism is low for ZPP(NP) and other lowness results. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 431–442. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Arvind, V., Kukur, P.P.: Graph isomorphism is in SPP. Inform. Comput. 204(5), 835–852 (2006)

    Article  MATH  Google Scholar 

  13. Köbler, J., Schoöning, U., Torán, J.: Graph isomorphism is low for PP. Comput. Complex. 2(4), 301–330 (1992)

    Article  MATH  Google Scholar 

  14. McKay, B.D.: Practical graph isomorphism. In: 10th Manitoba Conf. Numerical Mathematics and Computing (Winnipeg, 1980). Congressus Numerantium, vol. 30, pp. 45–86 (1981)

    Google Scholar 

  15. Cook, S.A.: The complexity of theorem-proving procedures. In: Proc. 3rd ACM Symp. Theory of Computing (STOC), pp. 151–158 (1971)

    Google Scholar 

  16. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman & Co (1979)

    Google Scholar 

  17. Gröger, H.D.: On the randomized complexity of monotone graph properties. Acta Cybernet. 10(3), 119–127 (1992)

    MATH  MathSciNet  Google Scholar 

  18. Ullman, J.R.: An algorithm for subgraph isomorphism. J. ACM 23(1), 31–42 (1976)

    Article  MATH  Google Scholar 

  19. Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, New York (1997)

    MATH  Google Scholar 

  20. Gindre, F., Trejo Pizzo, D.A., Barrera, G.: Daniela Lopez De Luise, M.: A criterion-based genetic algorithm solution to the jigsaw puzzle NP-complete problem. In: Proc. World Congress on Engineering and Computer Science (WCECS 2010), San Francisco (October 2010)

    Google Scholar 

  21. Goldberg, D., Malon, C., Bern, M.: A global approach to automatic solution of jigsaw puzzles. Comput. Geom. 28(2-3), 165–174 (2004)

    Article  MathSciNet  Google Scholar 

  22. Gwee, B.H., Lim, M.H.: Polyominoes tiling by a genetic algorithm. Comput. Optim. Appl. 6(3), 273–291 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Luks, E.M.: Isomorphism of graphs of bounded valence can be tested in polynomial time. J. Comput. Syst. Sci. 25, 42–65 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  24. Demaine, E.D., Demaine, M.L.: Jigsaw puzzles, edge matching, and polyomino packing: connections and complexity. Graphs Combin. 23(suppl. 1), 195–208 (2007)

    Google Scholar 

  25. Hall, P.: On representatives of subsets. J. London Math. Soc. 10(1), 26–30 (1935)

    Google Scholar 

  26. Halmos, P.R., Vaughan, H.E.: The marriage problem. Am. J. Math. 72, 214–215 (1950)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of IT, Monash University, Clayton, VIC, 3800, Australia

    Michael Brand

Authors
  1. Michael Brand
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Città Universitaria, Università degli Studi di Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Alfredo Ferro

  2. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Fabrizio Luccio

  3. Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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© 2014 Springer International Publishing Switzerland

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Brand, M. (2014). No Easy Puzzles: A Hardness Result for Jigsaw Puzzles. In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-07890-8_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07889-2

  • Online ISBN: 978-3-319-07890-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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