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Efficient Generation of Plane Triangulations without Repetitions

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Book cover Automata, Languages and Programming (ICALP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2076))

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Abstract

A “based” plane triangulation is a plane triangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all biconnected based plane triangulations with at most n vertices. The algorithm uses O(n) space and generates such triangulations in O(1) time per triangulation without duplications. The algorithm does not output entire triangulations but the difference from the previous triangulation. By modifying the algorithm we can generate all biconnected based plane triangulation having exactly n vertices including exactly r vertices on the outer face in O(1) time per triangulation without duplications, while the previous best algorithm generates such triangulations in O(n 2) time per triangulation. Also we can generate without duplications all biconnected (non-based) plane triangulations having exactly n vertices including exactly r vertices on the outer face in O(r 2 n) time per triangulation, and all maximal planar graphs having exactly n vertices in O(n 3) time per graph.

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References

  1. D. Avis, Generating rooted triangulations without repetitions, Algorithmica, 16, (1996), pp.618–632.

    MATH  MathSciNet  Google Scholar 

  2. T. Beyer and S. M. Hedetniemi, Constant time generation of rooted trees, SIAM J. Comput., 9, (1980), pp.706–712.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Chrobak and S. Nakano, Minimum-width grid drawings of plane graphs, Computational Geometry: Theory and Applications, 10, (1998), pp.29–54.

    MathSciNet  Google Scholar 

  4. H. de Fraysseix, J. Pach and R. Pollack, How to draw a planar graph on a grid, Combinatorica, 10, (1990), pp.41–51.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. A. Goldberg, Efficient algorithms for listing combinatorial structures, Cambridge University Press, New York, (1993).

    MATH  Google Scholar 

  6. J. E. Hopcroft and J.K. Wong, Linear time algorithm for isomorphism of planar graphs, Proc. of 6th STOC, (1974), pp.172–184.

    Google Scholar 

  7. D. L. Kreher and D. R. Stinson, Combinatorial algorithms, CRC Press, Boca Raton, (1998).

    Google Scholar 

  8. B. D. McKay, Isomorph-free exhaustive generation, J. of Algorithms, 26, (1998), pp.306–324.

    Article  MATH  MathSciNet  Google Scholar 

  9. W. Schnyder, Embedding planar graphs on the grid, Proc. 1st Annual ACM-SIAM Symp. on Discrete Algorithms, San Francisco, (1990), pp.138–148.

    Google Scholar 

  10. R. A. Wright, B. Richmond, A. Odlyzko and B. D. McKay, Constant time generation of free trees, SIAM J. Comput., 15, (1986), pp.540–548.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Gunma University, Kiryu, 376-8515, Japan

    Zhangjian Li & Shin-ichi Nakano

Authors
  1. Zhangjian Li
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  2. Shin-ichi Nakano
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Li, Z., Nakano, Si. (2001). Efficient Generation of Plane Triangulations without Repetitions. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_36

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  • DOI: https://doi.org/10.1007/3-540-48224-5_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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