On improved time bounds for permutation graph problems

  • Andreas Brandstädt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 657)


For many problems on permutation graphs, polynomial time bounds were found by using different approaches as e.g. dynamic programming, structural properties of the intersection model, the reformulation as a shortest-path problem on suitable derived graphs and a geometric representation as points in the plane. Here we outline these approaches and apply them to two problems: minimum weight independent dominating set and maximum weight cycle-free subgraph (minimum weight feedback vertex set).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. Arvind, C. Pandu Rangan: Connected domination and Steiner set on weighted permutation graphs, IPL 41 (1992), 215–220.Google Scholar
  2. 2.
    M.J. Atallah, S. Kosaraju: An Efficient Algorithm for Maxdominance with Applications, Algorithmica (1989) 4, 221–236.Google Scholar
  3. 3.
    M.J. Atallah, G.K. Manacher,J. Urrutia: Finding a minimum independent dominating set in a permutation graph, Discrete Applied Math., Vol 21, 177–183, 1988.Google Scholar
  4. 4.
    A. Brandstädt, D. Kratsch: On the restriction of some NP-complete graph problems to permutation graphs, L. Budach, ed., Proc. FCT 1985, Lecture Notes in Computer Science 199 (1985) 53–62, Fo.-erg. FSU Jena, N/84/80, 1984.Google Scholar
  5. 5.
    A. Brandstädt, D. Kratsch: On domination problems for permutation and other graphs, Theoretical Computer Science 54, 1987, 181–198.Google Scholar
  6. 6.
    C.J. Colbourn, L.K. Stewart: Permutation graphs: connected domination and Steiner trees, Topics on Domination, Annals of Discrete Mathematics 48 (Eds.: S.T. Hedetniemi, R.C. Laskar), 1990, 179–190.Google Scholar
  7. 7.
    D.G. Corneil, L.K. Stewart: Dominating sets in Perfect Graphs, Topics on Domination, Annals of Discrete Mathematics 48, 145–164.Google Scholar
  8. 8.
    S. Even, A. Pnueli, A. Lempel: Permutation graphs and transitive graphs, J. ACM, Vol 19, 400–410, 1972.Google Scholar
  9. 9.
    M. Farber, J.M. Keil: Domination in permutation graphs, J. Algorithms, Vol 6, 309–321, 1985.Google Scholar
  10. 10.
    V. Kamakoti, D. Kratsch, R. Mahesh, C. Pandu Rangan: A Unified Approach to Efficient Algorithms on weighted Permutation Graphs, manuscript 1991.Google Scholar
  11. 11.
    V. Kamakoti, C. Pandu Rangan: Efficient Transitive Reduction of Permutation graphs and its Applications, manuscript 1991.Google Scholar
  12. 12.
    H. Kim: Finding a maximum independent set in a permutation graph, Inf. Proc. Letters 36 (1990) 19–23.Google Scholar
  13. 13.
    E.L. Lawler: Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York 1976.Google Scholar
  14. 14.
    Y. Liang, C. Rhee, S.K. Dhall, S. Lakshmivarahan: A new approach for the domination problem on permutation graphs, Inf. Proc. Letters 37 (1991) 219–224.Google Scholar
  15. 15.
    G.K. Manacher, C.J. Smith, Efficient algorithms for new problems on interval graphs and interval models, manuscript, 1984.Google Scholar
  16. 16.
    A. Srinivasan, C. Pandu Rangan: Efficient algorithms for the minimum weighted dominating clique problem on permutation graphs, Theor. Comp. Sci. 91 (1991), 1–21.Google Scholar
  17. 17.
    A. Pnueli, A. Lempel, S. Even: Transitive orientation of graphs and identification of permutation graphs”, Canad.J. Math., Vol 23 (1971), 160–175.Google Scholar
  18. 18.
    J. Spinrad: On comparability and permutation graphs, SIAM J. Comput., Vol 14, 658–670, 1985.Google Scholar
  19. 19.
    J. Spinrad, A. Brandstädt, L. Stewart: Bipartite permutation graphs, Discrete Applied Math., Vol 18, 279–292, 1987.Google Scholar
  20. 20.
    K.H. Tsai, W.L. Hsu: Fast algorithms for the dominating set problem on permutation graphs, Internat. Sympos. SIGAL 1990, Lect. Notes in Comp. Sci. 450, 109–117.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  1. 1.Fachbereich Mathematik/FG InformatikUniversität-GH-DuisburgDuisburgGermany

Personalised recommendations