Advertisement

Treewidth and Dynamic Programming

  • Rodney G. Downey
  • Michael R. Fellows
Part of the Texts in Computer Science book series (TCS)

Abstract

A central concept in modern algorithm design uses the metaphor of treewidth, both in its original form for graphs, and its extensions to other areas. This chapter is devoted to developing the basic theory of treewidth, and fundamental aspects of producing treewidth algorithms by running dynamic programming on graphs.

Keywords

Dynamic Programming Constraint Satisfaction Problem Tree Decomposition Bayesian Belief Network Flow Control Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 23.
    J. Alber, F. Dorn, R. Niedermeier, Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs. Discrete Appl. Math. 145(2), 219–231 (2005) MathSciNetCrossRefMATHGoogle Scholar
  2. 44.
    S. Arnborg, D. Corneil, A. Proskurowski, Complexity of finding embeddings in a k-tree. SIAM J. Algebr. Discrete Methods 8(2), 277–284 (1987) MathSciNetCrossRefMATHGoogle Scholar
  3. 70.
    H. Bodlaender, Dynamic programming on graphs with bounded tree-width, in Proceedings of 15th International Colloquium on Automata, Languages and Programming (ICALP 1988), Tampere, Finland, July 11–15, 1988, ed. by T. Lepistö, A. Salomaa. LNCS, vol. 317 (Springer, Berlin, 1988), pp. 103–118 Google Scholar
  4. 73.
    H. Bodlaender, A tourist’s guide through treewidth, Technical Report RUU-CS-92-12, Department of Information and Computing Sciences, Utrecht University, The Netherlands, March 1992 Google Scholar
  5. 74.
    H. Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25(6), 1305–1317 (1996) MathSciNetCrossRefMATHGoogle Scholar
  6. 75.
    H. Bodlaender, Discovering treewidth, Technical Report RUU-CS-2005-18, Department of Information and Computing Sciences, Utrecht University, The Netherlands, 2005 Google Scholar
  7. 94.
    H. Bodlaender, T. Kloks, Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms 21(2), 358–402 (1996) MathSciNetCrossRefMATHGoogle Scholar
  8. 297.
    M. Fellows, M. Langston, Nonconstructive proofs of polynomial-time complexity. Inf. Process. Lett. 26, 157–162 (1987/88) MathSciNetCrossRefGoogle Scholar
  9. 329.
    J. Fouhy, Computational experiments on graph width metrics, Master’s thesis, Victoria University of Wellington, 2002 Google Scholar
  10. 341.
    F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs. J. Comb. Theory, Ser. B 16, 47–56 (1974) MathSciNetCrossRefMATHGoogle Scholar
  11. 458.
    A. Koster, S. van Hoesel, A. Kolen, Solving partial constraint satisfaction problems with tree decompositions. Networks 40(3), 170–180 (2002) MathSciNetCrossRefMATHGoogle Scholar
  12. 475.
    J. Lagergen, Algorithms and minimal forbidden minors for tree-decomposable graphs, PhD thesis, Department of Numerical Analysis and Computing Sciences, Royal Institute of Technology, Stockholm, Sweden, March 1991 Google Scholar
  13. 482.
    S. Lauritzen, D. Spiegelhalter, Local computations with probabilities on graphical structures and their applications to expert systems. J. R. Stat. Soc., Ser. B, Stat. Methodol. 50(2), 157–224 (1988) MathSciNetMATHGoogle Scholar
  14. 519.
    J. Matoušek, R. Thomas, Algorithms finding tree-decompositions of graphs. J. Algorithms 12, 1–22 (1991) MathSciNetCrossRefMATHGoogle Scholar
  15. 558.
    L. Perkovíc, B. Reed, An improved algorithm for finding tree decompositions of small width. Int. J. Found. Comput. Sci. 11(3), 365–371 (2000) CrossRefGoogle Scholar
  16. 575.
    B. Reed, Finding approximate separators and computing tree width quickly, in Proceedings of 24th ACM Symposium on Theory of Computing (STOC ’92), Victoria, British Columbia, Canada, May 4–May 6, 1992, ed. by R. Kosaraju, M. Fellows, A. Wigderson, J. Ellis (ACM, New York, 1992), pp. 221–228 Google Scholar
  17. 582.
    N. Robertson, P. Seymour, Graph minors—a survey, in Surveys in Combinatorics 1985 (Glasgow, 1985). London Mathematical Society Lecture Note Series, vol. 103 (Cambridge University Press, Cambridge, 1985), pp. 153–171 Google Scholar
  18. 588.
    N. Robertson, P. Seymour, Graph minors. XIII. The disjoint paths problem. J. Comb. Theory, Ser. B 63(1), 65–110 (1995) MathSciNetCrossRefMATHGoogle Scholar
  19. 589.
    N. Robertson, P. Seymour, Graph minors. XX. Wagner’s conjecture. J. Comb. Theory, Ser. B 92(2), 325–357 (2004) MathSciNetCrossRefMATHGoogle Scholar
  20. 594.
    D. Rose, R. Tarjan, G. Lueker, Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 266–283 (1976) MathSciNetCrossRefMATHGoogle Scholar
  21. 645.
    M. Thorup, All structured programs have small tree-width and good register allocation. Inf. Comput. 142(2), 159–181 (1998) MathSciNetCrossRefMATHGoogle Scholar
  22. 652.
    J. van Leeuwen, Graph algorithms, in Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, ed. by J. van Leeuwen (Elsevier/MIT Press, Amsterdam, 1990), pp. 525–631 Google Scholar
  23. 667.
    A. Yamaguchi, K. Aoki, H. Mamitsuka, Graph complexity of chemical compounds in biological pathways. Genome Inform. 14, 376–377 (2003) Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rodney G. Downey
    • 1
  • Michael R. Fellows
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

Personalised recommendations