Skip to main content
Log in

Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey

  • Part I Computer Science
  • Invited Paper
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A. V. Aho, J. E. Hopcroft and J. D. Ullman,Design and Analysis of Computer Algorithms, Reading, Mass. Addison-Wesley, 1974.

    Google Scholar 

  2. S. Arnborg,Reduced state enumeration — another algorithm for reliability evaluation, IEEE Trans. Reliability R-27 (1978), 101–105.

    Google Scholar 

  3. S. Arnborg,On the complexity of multivariable query evaluation, FOA Rapport C 20292-D8, National Defence Research Institute, Stockholm, Sweden (1979).

    Google Scholar 

  4. S. Arnborg, D. G. Corneil and A. Proskurowski,Complexity of finding embeddings in a k-tree, TRITA-NA 8407, Royal Institute of Technology, Sweden (1984).

    Google Scholar 

  5. S. Arnborg and A. Proskurowski,Characterization and recognition of partial k-trees, TRITA-NA 8402, Royal Institute of Technology, Sweden (1984).

    Google Scholar 

  6. S. Arnborg and A. Proskurowski,Linear time algorithms for NP-hard problems on graphs embedded in k-trees, TRITA-NA-8404, The Royal Institute of Technology (1984).

  7. B. Aspvall,Efficient algorithms for certain satisfiability and linear programming problems, PhD Thesis, STAN-CS-80-822, Stanford University, 1980.

  8. L. W. Beineke and R. E. Pippert,Properties and characterizations of k-trees, Mathematika 18 (1971), 141–151.

    Google Scholar 

  9. U. Bertele and F. Brioschi,Nonserial Dynamic Programming, Academic Press, New York, 1972.

    Google Scholar 

  10. C. J. Colbourn and A. Proskurowski,Concurrent transmissions in broadcast networks, in Proc. 11th Int'l Coll. on Automata, Languages, and Programming, Antwerp, Springer Verlag, Berlin (1984), 128–136.

    Google Scholar 

  11. D. G. Cornell and J. M. Keil,A dynamic programming approach to the dominating set problem on k-trees, Dept. of Computer Science, University of Toronto, Technical report (1983).

  12. D. G. Corneil, H. Lerchs and L. Stewart Burlingham,Complement reducible graphs, Discrete Appl. Math. 3 (1981), 163–174.

    Article  Google Scholar 

  13. M. Davis and H. Putnam,A computing procedure for quantification theory, J. ACM 7 (1960), 201–215.

    Article  Google Scholar 

  14. R. J. Duffin,Topology of series-parallel networks, J. Math. Anal. Appl. 10 (1965), 303–318.

    Article  Google Scholar 

  15. E. C. Freuder,Synthesizing constraint expressions, C. ACM 21 (1978), 958–966.

    Article  Google Scholar 

  16. M. R. Garey, R. L. Graham, D. S. Johnson and D. E. Knuth,Complexity results for bandwidth minimization, SIAM J. Appl. Math. 34 (1978), 835–859.

    Article  Google Scholar 

  17. M. R. Garey and D. S. Johnson,Computers and Intractability, W. H. Freeman and Company, San Francisco (1979).

    Google Scholar 

  18. F. Gavril,Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of chordal graph, SIAM J. Comput. 1 (1972), 180–187.

    Article  Google Scholar 

  19. G. Huet and D. Oppen,Equations and rewrite rules: a survey, in Formal Languages: Perspective and Open Problems (R. Book, Ed.), Academic Press, New York, 1980.

    Google Scholar 

  20. D. S. Johnson,The NP-Completeness column: an ongoing guide, J. of Algorithms 1–4 (1981–4).

  21. S. Kirkpatrick, C.D. Gelatt, Jr. and M. P. Vecchi,Optimization by simulated annealing, SCIENCE 220 (1983), 671–680.

    Google Scholar 

  22. D. Rose,Triangulated graphs and the elimination process, J. Math. Anal. Appl. 32, (1970), 597–609.

    Article  Google Scholar 

  23. D. Rose,On simple characterizations of k-trees, Discrete Math. 7 (1974), 317–322.

    Article  Google Scholar 

  24. A. Rosenthal,Computing the reliability of a complex network, SIAM J. Appl. Math. 32 (1977) 384–393.

    Article  Google Scholar 

  25. A. Rosenthal,Dynamic programming is optimal for nonserial optimization problems, SIAM J. Comput. 11 (1982), 47–59.

    Article  Google Scholar 

  26. A. Rosenthal,Series-parallel reduction for difficult measures of network reliability, NETWORKS 11 (1981), 323–334.

    Google Scholar 

  27. K. Takamizawa, T. Nishizeki and N. Saito,Linear-time computability of combinatorial problems on series-parallel graphs, J. ACM 29 (1982), 623–641.

    Article  Google Scholar 

  28. R. E. Tarjan,Decomposition by clique separators, Discrete Math., to appear.

  29. J. A. Wald and C. J. Colbourn,Steiner trees, partial 2-trees, and minimum IFI networks, Networks 13 (1983), 159–167.

    Google Scholar 

  30. D. L. Walz,Generating semantic descriptions from drawings of scenes with shadows. AI-TR-271, A.I. Lab, M.I.T., Cambridge, Mass., 1972.

    Google Scholar 

  31. S. H. Whitesides,An algorithm for finding clique cutsets, Inf. Proc. Letters 12 (1981), 31–32.

    Article  Google Scholar 

  32. M. Yannakakis,Computing the minimum fill-in is NP-complete, SIAM J. Alg. and Discr. Methods 2 (1981), 77–79.

    Google Scholar 

  33. M. Yannakakis,A polynomial algorithm for the MIN CUT LINEAR ARRANGEMENT of Trees, Proc. 24th Annual Symp. on Foundations of Computer Science, IEEE, 1983, 274–281.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arnborg, S. Efficient algorithms for combinatorial problems on graphs with bounded decomposability — A survey. BIT 25, 1–23 (1985). https://doi.org/10.1007/BF01934985

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01934985

Keywords

Navigation