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Dynamic programming on distance-hereditary graphs

  • Maw-Shang Chang
  • Sun-yuan Hsieh
  • Gen-Huey Chen
Session 7B
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)

Abstract

In this paper, we define a one-vertex-extension tree for a distance-hereditary graph and show how to build it. We then give a unified approach to designing efficient dynamic programming algorithms for distance-hereditary graphs based upon the one-vertex-extension tree, We give linear time algorithms for the weighted vertex cover and weighted independent domination problems and give an O(n2) time algorithm to compute a minimum fill-in and the treewidth for a distance-hereditary graph.

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References

  1. 1.
    S. Arnborg, D. G. Corneil, and A. Proskurowski.: Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Math. (1987) 277–284Google Scholar
  2. 2.
    H. J. Bandelt, A. Henkmann, and F. Nicolai.: Powers of distance-hereditary graphs. Technical Report SM-DU-220 (1993), University of DuisburgGoogle Scholar
  3. 3.
    H. J. Bandelt and H. M. Mulder: Distance-hereditary graphs. J. Comb. Theory. Series B. 41 (1986) 182–208Google Scholar
  4. 4.
    A. Branstadt and F. F. Dragan.: A linear-time algorithm for connected r-domination and Steiner tree on distance-hereditary graphs. Preprint (1994)Google Scholar
  5. 5.
    G. J. Chang.: Private communication.Google Scholar
  6. 6.
    M. S. Chang.: Weighted domination on cocomparability graphs. Lecture Notes in Computer Science. 1001 (1995) 122–131Google Scholar
  7. 7.
    A. D'atri and M. Moscarini. Distance-hereditary graphs, Steiner trees, and connected domination. SIAM J. Comput. 17 (1988) 521–538Google Scholar
  8. 8.
    F. F. Dragan. Dominating cliques in distance-hereditary graphs. Technical Report. SM-DU-248 (1994). University of DuisburgGoogle Scholar
  9. 9.
    A. H. Esfahanian and O. R. Oellermann. Distance-hereditary graphs and multidestination message-routing in multicomputers. JCMCC. 13 (1993) 213–222Google Scholar
  10. 10.
    S. T. Hedetniemi and R. C. Laskar. Bibliography on domination in graphs and some basic definitions of domination parameters. Disc. Math. 86 (1990) 257–277Google Scholar
  11. 11.
    P. L. Hammer and F. Maffray. Completely separable graphs. Disc. Appl. Math. 27 (1990) 85–99Google Scholar
  12. 12.
    E. Howorka. A characterization of distance-hereditary graphs. Quart. J. Math. Oxford (2) 28 (1977) 417–420Google Scholar
  13. 13.
    E. Howorka. A characterization of Ptolemaic graphs. J. Graph Theory. 5 (1981) 323–331Google Scholar
  14. 14.
    R. M. Karp. Reducibility among combinatorial problems. Plenum Press, New York, 1972Google Scholar
  15. 15.
    D. Kratsch and L. Stewart. Domination on cocomparability graphs. SIAM J. Disc. Math. 6 (1993), 400–417Google Scholar
  16. 16.
    H. Müller and F. Nicolai. Polynomial time algorithms for Hamiltonian problems on bipartite distance-hereditary graphs. Inform. Process. Lett. 46 (1993) 225–230Google Scholar
  17. 17.
    F. Nicolai. Hamiltonian problems on distance-hereditary graphs. Technical Report. SM-DU-264 (1994). University of DuisburgGoogle Scholar
  18. 18.
    C. Papadimitrious and M. Yannakakis. Optimization, approximation and complexity classes. Journal of Computer and System Science. (1991) 425–440Google Scholar
  19. 19.
    H. G. Yeh and G. J. Chang. Weighted connected domination and Steiner trees in distance-hereditary graphs. SubmittedGoogle Scholar
  20. 20.
    H. G. Yeh and G. J. Chang. Linear-time algorithms for bipartite distance-hereditary graphs. SubmittedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Maw-Shang Chang
    • 1
  • Sun-yuan Hsieh
    • 2
  • Gen-Huey Chen
    • 2
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityMin-Hsiun, ChiayiTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Taiwan UniversityTaipeiTaiwan

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