Abstract
In this paper we give an algorithm to generate all biconnected plane triangulations having exactly n vertices including exactly r vertices on the outer face. The algorithm uses O(n) space in total and generates such triangulations without duplications in O(rn) time per triangulation, while the previous best algorithm generates such triangulations in O(r 2 n) time per triangulation.
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Avis, D.: Generating rooted triangulations without repetitions. Algorithmica 16, 618–632 (1996)
Beyer, T., Hedetniemi, S.M.: Constant time generation of rooted trees. SIAM J. Comput. 9, 706–712 (1980)
Chrobak, M., Nakano, S.: Minimum-width grid drawings of plane graphs. Computational Geometry: Theory and Applications 10, 29–54 (1998)
de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10, 41–51 (1990)
Goldberg, L.A.: Efficient algorithms for listing combinatorial structures. Cambridge University Press, New York (1993)
Hopcroft, J.E., Wong, J.K.: Linear time algorithm for isomorphism of planar graphs. In: Proc. of 6th STOC, pp. 172–184 (1974)
Kreher, D.L., Stinson, D.R.: Combinatorial algorithms. CRC Press, Boca Raton (1998)
Li, Z., Nakano, S.: Efficient generation of plane triangulations without repetitions. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 433–443. Springer, Heidelberg (2001)
McKay, B.D.: Isomorph-free exhaustive generation. J. of Algorithms 26, 306–324 (1998)
Schnyder, W.: Embedding planar graphs on the grid. In: Proc. 1st Annual ACMSIAM Symp. on Discrete Algorithms, San Francisco, pp. 138–148 (1990)
Wright, R.A., Richmond, B., Odlyzko, A., McKay, B.D.: Constant time generation of free trees. SIAM J. Comput. 15, 540–548 (1986)
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Nakano, Si., Uno, T. (2004). More Efficient Generation of Plane Triangulations. In: Liotta, G. (eds) Graph Drawing. GD 2003. Lecture Notes in Computer Science, vol 2912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24595-7_25
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DOI: https://doi.org/10.1007/978-3-540-24595-7_25
Publisher Name: Springer, Berlin, Heidelberg
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