Linear time algorithms for k-cutwidth problem

  • Maw-Hwa Chen
  • Sing-Ling Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)


The Min Cut Linear Arrangement problem is to find a linear arrangement for a given graph such that the cutwidth is minimized. This problem has important applications in VLSI layout systems. It is known that this problem is NP-complete when the input is a general graph with maximum vertex degree at most 3. In this paper, we will first present a linear time algorithm to recognize the small cutwidth trees. The approach we used in this algorithm can then be easily extended to recognize the general graphs with cutwidth 3 in O(n) time.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Alok Aggarwal, Richard J. Anderson, and Ming Yanf Kao, “Parallel Depth-First search in general directed graphs,” SIAM J. Comput., Vol. 19, No. 2, April 1990, pp. 397–409.CrossRefGoogle Scholar
  2. [2]
    C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam 1973.Google Scholar
  3. [3]
    F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, Reading, 1990.Google Scholar
  4. [4]
    Fan R. K. Chung, “On the Cutwidth and the Topological Bandwidth of a Tree,” SIAM J. Alg. Disc. Meth., Vol. 6, No. 2, April 1985, pp. 268–277.Google Scholar
  5. [5]
    M. J. Chung, F. Makedon, I. H. Sudborough and J. Tarner, ”Polynomial algorithm for the min-cut linear arrangement problem on degree restricted trees,” SIAM J. Comput., Vol. 14, No. 1, 1985, pp. 158–177.Google Scholar
  6. [6]
    A. E. Dunlop and B. W. Kernighan, ”A Procedure for Placement of Standard-Cell VLSI Circuits,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, Vol. CAD-4, No. 1, Jan. 1985, pp. 92–98.CrossRefGoogle Scholar
  7. [7]
    M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Franciso 1979.Google Scholar
  8. [8]
    E. Gurari, and I. H. Sudborough, ”Improved dynamic programming algorithms for bandwidth minimization and min-cut linear arrangement problem,” J. Algorithms, Vol. 5, 1984, pp. 531–546.CrossRefGoogle Scholar
  9. [9]
    M. Y. Kao, ”All graphs have cycle separators and planar directed depth-first search is in DNC,” in Proc. 3rd Aegean Workship on Computing, Corfu, Greece, J. H. Reif, ed.; Lecture Notes in Computer Science 319, Springer-Verlay, Berlin, New York, 1988, pp. 53–63.Google Scholar
  10. [10]
    Thomas Lengauer, ”Upper and Lower Bounds on the Complexity of the Min-Cut Linear Arrangement Problem on Trees,” SIAM J. Alg. Disc. Meth., Vol. 3, No. 1, March 1982, pp. 99–113.Google Scholar
  11. [11]
    A. D. Lopez, and H. F. S. Law, ”A Dense Gate Matrix Layout Method for MOS VLSI,” IEEE Trans. on Electronic Devices, ED-27, 8, 1980, pp. 1671–1675.Google Scholar
  12. [12]
    F. S. Makedon, C. H. Papadimitriou and I. H. Sudborough, ”Topological Bandwidth,” SIAM J. Alg. Disc. Meth., Vol. 6, No. 3, July 1985, pp. 418–444.Google Scholar
  13. [13]
    Sanda L. Mitchell, ”Linear Algorithms to Recognize Oulplanar and Maximal Outerplanar Graphs,” Information Processing Letters, Vol. 9, No. 5, December 1979, pp. 229–232.CrossRefGoogle Scholar
  14. [14]
    T. H. Ohtsuki, H. Mori, E. S. Kuh, T. Kashiwabara and T. Fujiswa, ”One Dimensional Logic Gate Assignment and Interval Graphs,” IEEE Trans. Circuits and Systems, Vol. 26, 1979, pp. 675–684.CrossRefGoogle Scholar
  15. [15]
    A. L. Rosenberg, ”The Diogenes Approach to Testable Fault-Tolerant Arrays of Processors,” IEEE Trans. on Computers, Vol. C-32, No. 10, Oct. 1983, pp. 902–910.Google Scholar
  16. [16]
    R. E. Tarjan, ”An Efficient Parallel Biconnectivity Algorithm,” SIAM J. Comput., Vol. 14, No. 4, November 1985, pp. 862–874.MathSciNetGoogle Scholar
  17. [17]
    M. Yannakakis, ”A Polynomial Algorithm for the Min Cut Linear Arrangement of Trees,” J. ACM., Vol. 32, No. 4, 1985, pp. 950–988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Maw-Hwa Chen
    • 1
  • Sing-Ling Lee
    • 1
  1. 1.Institute of Computer Science and Information EngineeringNational Chung Cheng UniversityChaiyiTaiwan 62107, ROC

Personalised recommendations