Advertisement

Algorithms for maximum matching and minimum fill-in on chordal bipartite graphs

  • Maw-Shang Chang
Session 4b: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)

Abstract

We define an ordering of vertices of a chordal bipartite graph. By using this ordering, we give a linear time algorithm for the maximum matching problem and an O(n4) time algorithm for the minimum fill-in problem on chordal bipartite graphs improving previous results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Bodlaender, T. Kloks, D. Kratsch, and H. Müller, Treewidth and minimum fill-in on d-trapezoid graphs, Technical Report UU-CS-1995-34, Utrecht University.Google Scholar
  2. 2.
    A. Brandstädt, Classes of bipartite graphs related to chordal graphs, Discrete Appl. Math. 32 (1991) 51–60.CrossRefGoogle Scholar
  3. 3.
    D. G. Corneil, Y. Perl, and L. K. Stewart, Cographs: recognition, applications, and algorithms, Congressus Numerantium, 43 (1984) 249–258.Google Scholar
  4. 4.
    M. Farber, Characterization of strongly chordal graphs, Discrete Math. 43 (1983) 173–189.CrossRefGoogle Scholar
  5. 5.
    F. Gavril, Algorithms for maximum k-colorings and k-coverings of transitive graphs, Networks 17 (1987) 465–470.Google Scholar
  6. 6.
    J. E. Hopcroft and R. M. Karp, A n 5/2 algorithm for maximum matching in bipartite graphs, SIAM J. Comput. 2 (1973) 225–231.CrossRefGoogle Scholar
  7. 7.
    T. Kloks, Minimum fill-in for chordal bipartite graphs, Technical report RUU-CS-93-11, Department of CS, Utrecht Universtity, Utrecht The Netherlands (1993).Google Scholar
  8. 8.
    T. Kloks, D. Kratsch, and C. K. Wong, Minimum fill-in on circle and circular-arc graphs, To appear in the proceedings of ICALP'96.Google Scholar
  9. 9.
    A. Parra, Triangulating multitolerance graphs, Technical Report, 392/1994, Technische Universität Berlin.Google Scholar
  10. 10.
    D. J. Rose, Triangulated graphs and the elimination process, J. Math. Anal. Appl. 32 (1970) 597–609.CrossRefGoogle Scholar
  11. 11.
    D. J. Rose, A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations, in: Graph Theory and Computing, R. Read, (ed.), Academic Press, New York, (1973) 183–217.Google Scholar
  12. 12.
    J. P. Spinrad, Doubly lexical ordering of dense 0–1 matrices, Information Processing Letters 45 (1993) 229–235.CrossRefGoogle Scholar
  13. 13.
    J. P. Spinrad, A. Brandstädt, and L. Stewart, Bipartite permutation graphs, Discrete Appl. Math. 18 (1987) 279–292.CrossRefGoogle Scholar
  14. 14.
    R. E. Tarjan, Decomposition by clique seperators, Discrete Math. 55 (1985) 221–232.CrossRefGoogle Scholar
  15. 15.
    M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1981) 77–79.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Maw-Shang Chang
    • 1
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityChiayiTaiwan Republic of China

Personalised recommendations