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Boundary Matching for Interactive Sprouts

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Advances in Computer Games (ACG 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9525))

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Abstract

The simplicity of the pen-and-paper game Sprouts hides a surprising combinatorial complexity. We describe an optimization called boundary matching that accommodates this complexity to allow move generation for Sprouts games of arbitrary size at interactive speeds.

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Notes

  1. 1.

    Number of paths incident with vertex \(v_i\).

  2. 2.

    http://sprouts.tuxfamily.org/wiki/doku.php?id=records.

  3. 3.

    The app did not work on any device tested.

  4. 4.

    Denis Mollison’s analysis of the \(n=6\) game famously ran to 47 pages [2, p. 602].

  5. 5.

    Except for \(O_{1}^{+}\) = 1.

  6. 6.

    We prefer to use the full term “canonicalization” rather than the abbreviation “canonization”; we do not claim that the algorithms perform miracles.

  7. 7.

    http://sprouts.tuxfamily.org/wiki/doku.php?id=home.

  8. 8.

    The early, mid and end games could be described as approximately covering moves \(1 \dots n-1, n \dots 2n-1\) and \(2n \dots 3n-1\), respectively, on average.

References

  1. Applegate, D., Jacobson, G., Sleator, D.: Computer Analysis of Sprouts. Technical report CMU-CS-91-144, Carnegie Mellon University Computer Science Technical Report (1991)

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  2. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 3, 2nd edn. AK Peters, Natick (2001)

    MATH  Google Scholar 

  3. Department of Mathematics, University of Utah: The Game of Sprouts. http://www.math.utah.edu/~pa/Sprouts

  4. Focardi, R., Luccio, F.L.: A modular approach to sprouts. Discrete Appl. Math. 144(3), 303–319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gardner, M.: Mathematical games: of sprouts and brussels sprouts; games with a topological flavour. Sci. Am. 217(1), 112–115 (1967)

    Article  Google Scholar 

  6. Gehrig, D.: Sprouts - A Game of Maths!. https://itunes.apple.com/au/app/spouts-a-game-of-maths!/id426618463?mt=8

  7. Lemoine, J., Viennot, S.: Computer Analysis of Sprouts with Nimbers. Technical report, arXiv:1008.2320v1 (2011)

  8. Reiß, S.: 3Graph. http://www.reisz.de/3graph_en.htm

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Acknowledgments

This work was funded by a QUT Vice-Chancellor’s Research Fellowship as part of the project Games Without Frontiers.

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Authors and Affiliations

  1. Queensland University of Technology, Gardens Point, Brisbane, 4000, Australia

    Cameron Browne

Authors
  1. Cameron Browne
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Correspondence to Cameron Browne .

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Editors and Affiliations

  1. Leiden University , Leiden, The Netherlands

    Aske Plaat

  2. Leiden University , Leiden, The Netherlands

    Jaap van den Herik

  3. Leiden University , Leiden, The Netherlands

    Walter Kosters

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© 2015 Springer International Publishing Switzerland

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Browne, C. (2015). Boundary Matching for Interactive Sprouts. In: Plaat, A., van den Herik, J., Kosters, W. (eds) Advances in Computer Games. ACG 2015. Lecture Notes in Computer Science(), vol 9525. Springer, Cham. https://doi.org/10.1007/978-3-319-27992-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-27992-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27991-6

  • Online ISBN: 978-3-319-27992-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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