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Solving General Lattice Puzzles

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Frontiers in Algorithmics (FAW 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6213))

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Abstract

In this paper we describe implementations of two general methods for solving puzzles on any structured lattice. We define the puzzle as a graph induced by (finite portion of) the lattice, and apply a back-tracking method for iteratively find all solutions by identifying parts of the puzzle (or transformed versions of them) with subgraphs of the puzzle, such that the entire puzzle graph is covered without overlaps by the graphs of the parts. Alternatively, we reduce the puzzle problem to a submatrix-selection problem, and solve the latter problem by using the “dancing-links” trick of Knuth. A few expediting heuristics are discussed, and experimental results on various lattice puzzles are presented.

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References

  1. De Bruijn, N.G.: Programmeren van de pentomino puzzle. Euclides 47, 90–104 (1971–1972)

    Google Scholar 

  2. Demaine, E.D., Demaine, M.L.: Jigsaw puzzles, edge matching, and polyomino packing: Connections and complexity. Graphs and Combinatorics 23(suppl.), 195–208 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dudeney, H.E.: 74.—The broken chessboard. In: The Canterbury Puzzles, 90–92 (1908)

    Google Scholar 

  4. Fletcher, J.G.: A program to solve the pentomino problem by the recursive use of macros. Comm. of the ACM 8, 621–623 (1965)

    Article  Google Scholar 

  5. Gardner, M.: Mathematical games: More about complex dominoes, plus the answers to last month;s puzzles. Scientific American 197, 126–140 (1957)

    Article  Google Scholar 

  6. Garey, M., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  7. Golomb, S.W.: Checkerboards and polyominoes. American Mathematical Monthly 61, 675–682 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  8. Golomb, S.W.: Polyominoes, Scribners, New York (1965); 2nd edn. Princeton University Press, Princeton (1994)

    Google Scholar 

  9. Golomb, S.W., Baumart, L.D.: Backtrack programming, J. J. of the ACM 12, 516–524 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. Haselgrove, C.B., Haselgrove, J.: A computer program for pentominoes. Eureka 23, 16–18 (1960)

    Google Scholar 

  11. Haselgrove, J.: Packing a square with Y-pentominoes. J. of Recreational Mathematics 7, 229 (1974)

    Google Scholar 

  12. Knuth, D.E.: Dancing links. In: Davies, J., Roscoe, B., Woodcock, J. (eds.) Millennial Perspectives in Computer Science, pp. 187–214. Palgrave Macmillan, England (2000), http://arxiv.org/abs/cs/0011047

    Google Scholar 

  13. Lewis, H.R.: Complexity of solvable cases of the decision problem for the predicate calculus. In: 19th Ann. Symp. on Foundations of Computer Science, Ann Arbor, MI, pp. 35–47 (1978)

    Google Scholar 

  14. Meeus, J.: Some polyomino and polyamond problems. J. of Recreational Mathematics 6, 215–220 (1973)

    MathSciNet  MATH  Google Scholar 

  15. Scott, D.S.: Programming a combinatorial puzzle, Technical Report 1, Dept. of Electrical Engineering, Princeton University (June 1958)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Center for Graphics and Geometric Computing, Dept. of Computer Science, Technion, Israel Institute of Technology, Haifa, 32000, Israel

    Gill Barequet

  2. Dept. of Computer Science, The Open University, Raanana, Israel

    Shahar Tal

Authors
  1. Gill Barequet
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  2. Shahar Tal
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Editor information

Editors and Affiliations

  1. Academia Sinica, Institute of Information Science 20, Section 2, 128 Academia Road, Nankang, 11529, Taipei, Taiwan

    Der-Tsai Lee

  2. Department of Computer Science and Engineering, University of Notre Dame, 46556, Notre Dame, IN, USA

    Danny Z. Chen

  3. State Key Laboratory of Software Engineering, Wuhan University, 430072, Wuhan, Hubei, China

    Shi Ying

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© 2010 Springer-Verlag Berlin Heidelberg

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Barequet, G., Tal, S. (2010). Solving General Lattice Puzzles. In: Lee, DT., Chen, D.Z., Ying, S. (eds) Frontiers in Algorithmics. FAW 2010. Lecture Notes in Computer Science, vol 6213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14553-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-14553-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14552-0

  • Online ISBN: 978-3-642-14553-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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