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Relational Modelling and Solution of Chessboard Problems

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Relational and Algebraic Methods in Computer Science (RAMICS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6663))

Abstract

We describe a simple computing technique for solving independence and domination problems on rectangular chessboards. It rests upon relational modelling and uses the BDD-based tool RelView for the evaluation of the relation-algebraic expressions that specify the problems’ solutions and the visualization of the computed results. The technique described in the paper is very flexible and especially appropriate for experimentation. It can easily be applied to other chessboard problems.

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References

  1. Bell, J., Stevens, B.: A survey of known results and research areas for n queens. Discr. Math. 309, 1–31 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berghammer, R., Neumann, F.: RelView – An OBDD-Based Computer Algebra System for Relations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Berghammer, R.: Applying relation algebra and RelView to solve problems on orders and lattices. Acta. Infor. 45, 211–236 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Berghammer, R., Rusinowska, A., de Swart, H.: An interdisciplinary approach to coalition formation. Europ. J. Operat. Res. 195, 487–496 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Berghammer, R., Rusinowska, A., de Swart, H.: Applying relation algebra and RelView to measures in a social network. EJOR 202, 182–198 (2010)

    Article  MATH  Google Scholar 

  6. Bryant, R.E.: Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Comput. Surv. 24, 293–318 (1992)

    Article  Google Scholar 

  7. Chen, H.-C., Ho, T.-Y.: The rook problem on saw-toothed chessboards. Appl. Math. Lett. 21, 1234–1237 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cockayne, E.J.: Chessboard domination problems. Discr. Math. 86, 13–20 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gibbons, P.B., Webb, J.A.: Some new results for the queens domination problem. Austral. J. of Combinat. 15, 145–160 (1997)

    MathSciNet  MATH  Google Scholar 

  10. de Jaenisch, C.F.: Applications de l’analyse mathematiques au jeu des echecs. Petrograd (1882)

    Google Scholar 

  11. Leoniuk, B.: ROBDD-basierte Implementierung von Relationen und relationalen Operationen mit Anwendungen. Dissertation, Universität Kiel (2001)

    Google Scholar 

  12. Milanese, U.: Zur Implementierung eines ROBDD-basierten Systems für die Manipulation und Visualisierung von Relationen. Dissertation, Universität Kiel (2003)

    Google Scholar 

  13. Nauck, F.: Briefwechsel mit allen für alle. Illustrierte Zeitung 15, 182 (1850)

    Google Scholar 

  14. Pauls, E.: Das Maximalproblem der Damen auf dem Schachbrett. Deutsche Schachzeitung 29, 129–134 (1874)

    Google Scholar 

  15. Schmidt, G., Ströhlein, T.: Relations and graphs. Discrete Mathematics for Computer Scientists. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  16. Steinbach, B., Posthoff, C.: New results based on Boolean models. In: Steinbach, B. (ed.) Proc. 9th Int. Workshop on Boolean Problems, TU Freiberg, pp. 29–36. (2010)

    Google Scholar 

  17. Watkins, J.J.: Across the board: The mathematics of chessboard problems. Princeton University Press, Princeton (2004)

    Book  MATH  Google Scholar 

  18. Yaglom, A.M., Yaglom, I.M.: Challenging mathematical problems with elementary solutions, vol. I. Holden-Day Inc. (1964)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität Kiel, Olshausenstraße 40, D-24098, Kiel, Germany

    Rudolf Berghammer

Authors
  1. Rudolf Berghammer
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

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Berghammer, R. (2011). Relational Modelling and Solution of Chessboard Problems. In: de Swart, H. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2011. Lecture Notes in Computer Science, vol 6663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21070-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-21070-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21069-3

  • Online ISBN: 978-3-642-21070-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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