Dynamic algorithms for graphs with treewidth 2

  • Hans L. Bodlaender
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 790)


In this paper, we consider algorithms for maintaining treedecompositions with constant bounded treewidth under edge and vertex insertions and deletions for graphs with treewidth at most 2 (also called: partial 2-trees, or series-parallel graphs), and for almost trees with parameter k. Each operation can be performed in O(log n) time. For a large number of graph decision, optimization and counting problems, information can be maintained using O(log n) time per update, such that queries can be resolved in O(log n) or O(1) time. Similar results hold for the classes of almost trees with parameter k, for fixed k.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. R. Abrahamson and M. R. Fellows. Finite automata, bounded treewidth and well-quasiordering. In Graph Structure Theory, Contemporary Mathematics vol. 147, pages 539–564. American Mathematical Society, 1993.Google Scholar
  2. 2.
    S. Arnborg, J. Lagergren, and D. Seese. Easy problems for tree-decomposable graphs. J. Algorithms, 12:308–340, 1991.Google Scholar
  3. 3.
    H. L. Bodlaender. NC-algorithms for graphs with small treewidth. In J. van Leeuwen, editor, Proc. Workshop on Graph-Theoretic Concepts in Computer Science WG'88, pages 1–10. Springer Verlag, Lecture Notes in Computer Science, vol. 344, 1988.Google Scholar
  4. 4.
    H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. In Proceedings of the 25th Annual Symposium on Theory of Computing, pages 226–234. ACM Press, 1993.Google Scholar
  5. 5.
    H. L. Bodlaender and T. Kloks. A simple linear time algorithm for triangulating threecolored graphs. J. Algorithms, 15:160–172, 1993.Google Scholar
  6. 6.
    R. B. Borie, R. G. Parker, and C. A. Tovey. Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families. Algorithmica, 7:555–582, 1992.Google Scholar
  7. 7.
    N. Chandrasekharan. Fast Parallel Algorithms and Enumeration Techniques for Partial k-Trees. PhD thesis, Clemson University, 1990.Google Scholar
  8. 8.
    R. F. Cohen, S. Sairam, R. Tamassia, and J. S. Vitter. Dynamic algorithms for bounded tree-width graphs. Technical Report CS-92-19, Department of Computer Science, Brown University, 1992.Google Scholar
  9. 9.
    D. Fernández-Baca and G. Slutzki. Parametic problems on graphs of bounded treewidth. In O. Nurmi and E. Ukkonen, editors, Proceedings 3rd Scandinavian Workshop on Algorithm Theory, pages 304–316. Springer Verlag, Lecture Notes in Computer Science, vol. 621, 1992.Google Scholar
  10. 10.
    G. N. Frederickson. A data structure for dynamically maintaining rooted trees. In Proceedings of the 4th ACM-SIAM Symposium on Discrete Algorithms, pages 175–184, 1993.Google Scholar
  11. 11.
    G. N. Frederickson. Maintaining regular properties dynamically in k-terminal graphs. Manuscript, 1993.Google Scholar
  12. 12.
    J. Lagergren. Efficient parallel algorithms for tree-decomposition and related problems. In Proceedings of the 31rd Annual Symposium on Foundations of Computer Science, pages 173–182, 1990.Google Scholar
  13. 13.
    J. Matousěk and R. Thomas. Algorithms finding tree-decompositions of graphs. J. Algorithms, 12:1–22, 1991.Google Scholar
  14. 14.
    G. L. Miller and J. Reif. Parallel tree contraction and its application. In Proceedings of the 26th Annual Symposium on Foundations of Computer Science, pages 478–489, 1985.Google Scholar
  15. 15.
    B. Reed. Finding approximate separators and computing tree-width quickly. In Proceedings of the 24th Annual Symposium, on Theory of Computing, pages 221–228, 1992.Google Scholar
  16. 16.
    N. Robertson and P. D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms, 7:309–322, 1986.Google Scholar
  17. 17.
    J. van Leeuwen. Graph algorithms. In Handbook of Theoretical Computer Science, A: Algorithms and Complexity Theory, pages 527–631, Amsterdam, 1990. North Holland Publ. Comp.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  1. 1.Department of Computer ScienceUtrecht UniversityTB Utrechtthe Netherlands

Personalised recommendations