Linear-time heuristics for minimum weight rectangulation

  • Christos Levcopoulos
  • Anna Östlin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1097)


We consider the problem of partitioning rectilinear polygons into rectangles, using segments of minimum total length. This problem is NP-hard for polygons with holes. Even for hole-free polygons no known algorithm can find an optimal partitioning in less than O(n4) time.

We present the first linear-time algorithm for computing rectangulations of hole-free polygons, within a constant factor of the optimum. We achieve this result by deriving a linear-time algorithm for producing rectangulations of histograms of length less than 2.42 times the optimum, and then solving the problem of producing a proper partition into histograms.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chazelle, B.: Triangulating a Simple Polygon in Linear Time. Proc. 31st Symp. on Foundations of Computer Science, pp. 220–230, 1990.Google Scholar
  2. 2.
    Chin, F., Snoeyink, J., Wang, C.A.: Finding the Medial Axis of a Simple Polygon in Linear Time. Proc., 6th International Symposium on Algorithms and Computation, ISAAC '95, Cairns, Australia, 1995. (LNCS 1006, Springer Verlag).Google Scholar
  3. 3.
    Gabow, H., Bentley, J., Tarjan, R.: Scaling and Related Techniques for Geometry Problems. Proc. 16th Annual ACM Symposium on Theory of Computing, pp. 135–143, April 1984.Google Scholar
  4. 4.
    Gonzalez, T, Zheng, S.Q.: Bounds for Partitioning Rectilinear Polygons. Proc. First ACM Symposium on Computional Geometry, Baltimore, June 1985.Google Scholar
  5. 5.
    Harel, D., Tarjan, R.E.: Fast Algorithms for Finding Nearest Common Ancestors. SIAM Journal of Computing, Vol. 13, No. 2, May 1984.Google Scholar
  6. 6.
    Levcopoulos, C.: Minimum Length and “Thickest-first” Rectangular partitions of Polygons. Proc. 20th Allerton Conf. on Comm. Control and Compt., Monticello, Illinois, 1982.Google Scholar
  7. 7.
    Levcopoulos, C.: Fast Heuristics for Minimum Length Rectangular Partitions of Polygons. In Proc. of the 2nd ACM Symp. on Comp. Geomety, pp. 100–108, 1986.Google Scholar
  8. 8.
    Levcopoulos, C.: Heuristics for Minimum Decompositions of Polygons. PhD dissertation no. 155, Linköping University, 1987.Google Scholar
  9. 9.
    Levcopoulos, C., Östlin, A.: Linear-Time Heuristics for Minimum Weight Rectangulation. Technical Report LU-CS-TR:96-165, Lund University, 1996.Google Scholar
  10. 10.
    Lingas, A.: Heuristics for Minimum Edge Length Rectangular Partitions of Rectilinear Figures. Proc. 6th GI-Conference, Dortmund, January 1983. (LNCS 145, Springer Verlag).Google Scholar
  11. 11.
    Levcopoulos, C., Lingas, A.: Bounds on the Length of Convex Partitions of Polygons. Proc. 4th Conference on Found. of Software Technology and Theoretical Computer Science, Bangalore, India, 1984. (LNCS 181, Springer Verlag).Google Scholar
  12. 12.
    Lingas, A., Pinter, R.Y., Rivest, R.L. Shamir, A.: Minimum Edge Length Partitioning of Rectilinear Polygons. Proc. 20th Allerton Conf. on Comm. Control and Compt., Monticello, Illinois, 1982.Google Scholar
  13. 13.
    Vuillemin, J.: A Unifying Look at Data Structures. Communications of the ACM, Vol. 23 (4), April 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Anna Östlin
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden

Personalised recommendations