Skip to main content
SpringerLink
Log in

A theory of rectangular dual graphs

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Arectangular graph is a plane graph where all regions are four-sided and all edges are oriented in either the vertical or the horizontal direction. In addition the graph enclosure must also be rectangular. Given a plane graph representing a desired component connectivity, itsrectangular dual can be used to build afloorplan. This indicates that a system implementation can allocate rectangular floorplan regions to components that can be pairwise connected through common borders.

This paper proves that constructing a rectangular dual graph is equivalent to a matching problem in a bipartite graph derived from the given plane graph. A simple existence theorem in terms of the graph structure is obtained as a corollary.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Grason, An Approach to Computerized Space Planning Using Graph Theory,Proc. Design Automation Workshop, 1971, pp. 170–176.

  2. W. R. Heller, G. Sorkin, and K. Maling, The Planar Package Planner for System Designers,Proc. 19th Design Automation Conference, 1982, pp. 253–260.

  3. P. Bruell, Microelectronics and Computer Technology Corporation, private communication.

  4. D. T. Lee, Two-Dimensional Voronoi Diagrams in theL itp-Metric,J. Assoc. Comput. Mach., Vol. 27, No. 4, 1980, pp. 604–618.

    MATH  MathSciNet  Google Scholar 

  5. O. Ore,The Four-Color Problem, Academic Press, New York, 1967.

    MATH  Google Scholar 

  6. M. V. Swany and K. Thulasiramn,Graphs, Networks, and Algorithms, Wiley Interscience, New York, 1981.

    Google Scholar 

  7. S. Even,Graph Algorithms, Computer Science Press, Rockville, MD.

  8. J. Hopcroft and R. M. Karp, Ann 2 1/2 Algorithm for Maximum Matching in Bipartite Graphs,SIAM J. Comput., 1975, pp. 225–231.

  9. A. Itai, M. Rodeh, and S. L. Tanimoto, Some Matching Problems for Bipartite Graphs,J. Assoc. Comput. Mach., Vol. 24, No. 24, 1978, pp. 517–525.

    MathSciNet  Google Scholar 

  10. J. Bhasker and S. Sahni, A Linear Algorithm to Find a Rectangular Dual of a Planar Triangulated Graph,Proc. 23rd Design Automation Conference, 1986, pp. 108–114.

  11. K. Kozminski and E. Kinnen, Rectangular Duals of Planar Graphs,Networks, Vol. 15, 1985, pp. 145–157.

    Article  MATH  MathSciNet  Google Scholar 

  12. P. Rosentiehl and R. E. Tarjan, Rectilinear Planar Layouts of Planar Graphs and Bipolar Orientations,Discrete Comput. Geom., Vol. 1, No. 4, 1986, pp. 342–351.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, National Chen-Kung University, Tainan, Taiwan

    Yen-Tai Lai

  2. SRI International, CSL, 333 Ravenswood Avenue, 94025, Menlo Park, CA, USA

    Sany M. Leinwand

Authors
  1. Yen-Tai Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sany M. Leinwand
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by D. T. Lee.

This work was supported by the National Science Council, Taiwan, Republic of China, under Contract NSC 78-0404-E006-14.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lai, YT., Leinwand, S.M. A theory of rectangular dual graphs. Algorithmica 5, 467–483 (1990). https://doi.org/10.1007/BF01840399

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01840399

Key words

Search

Navigation