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Enumerating Floorplans with n Rooms

  • Shin-ichi Nakano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2223)

Abstract

A plane drawing of a graphis called a floorplan if every face (including the outer face) is a rectangle. A based floorplan is a floorplan with a designated base line segment on the outer face. In this paper we give a simple algorithm to generate all based floorplans with at most n faces. The algorithm uses O(n) space and generates such. oorplans in O(1) time per floorplan without duplications. The algorithm does not output entire floorplans but the difference from the previous floorplan. By modifying the algorithm we can generate without duplications all based floorplans having exactly n faces in O(1) time per floorplan. Also we can generate without duplications all (non-based) floorplans having exactly n faces in O(n) time per floorplan.

Keyword

Graphs Plane graphs Enumeration Listing 

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References

  1. 1.
    D. Avis, Generating rooted triangulations without repetitions, Algorithmica, 16, (1996) 618–632.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    T. Beyer and S. M. Hedetniemi, Constant time generation of rooted trees, SIAM J. Comput., 9, (1980) 706–712.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    L. A. Goldberg, Efficient algorithms for listing combinatorial structures, Cambridge University Press, New York, (1993).CrossRefMATHGoogle Scholar
  4. 4.
    D. L. Kreher and D. R. Stinson, Combinatorial algorithms, CRC Press, Boca Raton, (1998).Google Scholar
  5. 5.
    Z. Li and S. Nakano, Efficient Generation of Plane Triangulations without Repetitions, Proc. of ICALP 2001, LNCS2076, (2001) 433–443.MATHGoogle Scholar
  6. 6.
    B. D. McKay, Isomorph-free exhaustive generation, J. of Algorithms, 26, (1998) 306–324.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    R. A. Wright, B. Richmond, A. Odlyzko and B. D. McKay, Constant time generation of free trees, SIAM J. Comput., 15, (1986) 540–548.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Shin-ichi Nakano
    • 1
  1. 1.Gunma UniversityKiryuJapan

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