Skip to main content
SpringerLink
Log in

On heuristics for minimum length rectilinear partitions

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

The problem of partitioning a rectilinear figure into rectangles with minimum length is NP-hard and has bounded heuristics. In this paper we study a related problem,Elimination Problem (EP), in which a rectilinear figure is partitioned into a set of rectilinear figures containing no concave vertices of a fixed direction with minimum length. We show that a heuristic for EP within a factor of 4 from optimal can be computed in timeO(n 2), wheren is the number of vertices of the input figure, and a variant of this heuristic, within a factor of 6 from optimal, can be computed in timeO(n logn). As an application, we give a bounded heuristic for the problem of partitioning a rectilinear figure into histograms of a fixed direction with minimum length.

An auxiliary result is that an optimal rectangular partition of a monotonic histogram can be computed in timeO(n 2), using a known speed-up technique in dynamic programming.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. Z. Du, On Fast Heuristics for Minimum Edge Length Rectangular Partition, Technique Report-03618-86, Mathematical Sciences Research Institute, Berkeley, CA, 1986.

    Google Scholar 

  2. D. Knuth, Optimum binary search trees,Acta Inform.,1 (1971), 14–25.

    Article  MATH  Google Scholar 

  3. D. T. Lee and F. P. Preparata, Computational geometry: a survey,IEEE Trans. Comput.,33 (1984), 1072–1101.

    Article  MathSciNet  Google Scholar 

  4. C. Levcopoulos, Minimum length and thickest first rectangular partition of polygons,Proc. 23rd Allerton Conf. on Comm. Control and Computing, Illinois, 1985, pp. 664–673.

  5. A. Lingas,Heuristics for Minimum Edge Length Rectangular Partition of Rectilinear Figures, Lecture Notes on Computer Science, vol. 195, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  6. A. Lingas, R. Pinter, R. Rivest, and A. Shamir, Minimum edge length decomposition of rectilinear figures,20th Allerton Conf. on Comm. Control and Computing, Illinois, 1982, pp. 53–63.

  7. E. Lodi, F. Luccio, C. Mugnai, L. Pagli, and W. Lipski, On two-dimensional data organization 2,Fund. Inform.,2 (1979), 245–260.

    MATH  MathSciNet  Google Scholar 

  8. F. Yao, Speed-up in dynamic programming,SIAM J. Algebraic Discrete Methods,3 (1982), 532–540.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Academia Sinica, Beijing, People's Republic of China

    Dingzhu Du

  2. Computer Science Division, University of California, 94720, Berkeley, CA, USA

    Yanjun Zhang

Authors
  1. Dingzhu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanjun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by D. T. Lee.

Part of this work was done when the first author was a postdoctor fellow in MSRI, Berkeley, and supported in part by NSF Grant No. 8120790. The second author was supported in part by NSF Grant No. DCR-8411945.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Du, D., Zhang, Y. On heuristics for minimum length rectilinear partitions. Algorithmica 5, 111–128 (1990). https://doi.org/10.1007/BF01840380

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01840380

Key words

Search

Navigation