Skip to main content

Faster algorithms for subgraph isomorphism of κ-connected partial κ-trees

  • Conference paper
  • First Online:
Algorithms — ESA '96 (ESA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1136))

Included in the following conference series:

Abstract

The problem of determining whether a k-connected partial k-tree is isomorphic to subgraph of another k-connected partial k-tree is shown to be solvable in time O(n k+2). For k=2, and k=3, the stronger time-bound of O(n 3.5) is obtained. The presented time-bounds considerably improve the corresponding bounds known in the literature. They rely in part on a new characterization of width-k tree-decomposition of k-connected partial k-trees.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Arnborg, J. Lagergren, D. Seese. Problems easy for tree-decomposable graphs. Journal of Algorithms, 12 (1991), pp. 308–340.

    Google Scholar 

  2. S. Arnborg, A. Proskurowski. Linear time algorithms for NP-hard problems on graphs embedded in k-trees. Discrete Applied Mathematics 23 (1989), pp. 11–24.

    Google Scholar 

  3. H. Bodlaender. Dynamic programming on graphs with bounded tree-width. Proc. ICALP'88, LNCS 317, pp. 105–118, Springer Verlag.

    Google Scholar 

  4. H. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. Proc. 33rd ACM STOC, pp. 226–234.

    Google Scholar 

  5. M.R. Garey, D.S. Johnson. Computers and Intractability. A Guide to the Theory of NP-completeness. Freeman, San Francisco, 1979.

    Google Scholar 

  6. A. Gupta, N. Nishimura. Sequential and Parallel Algorithms for Embedding Problems on Classes of Partial k-Trees. Proc. SWAT'94, LNCS 824, pp. 172–182, Springer Verlag.

    Google Scholar 

  7. A. Gupta, N. Nishimura. Characterizing the Complexity of Subgraph Isomorphism for Graphs of Bounded Path-Width. Proc. STACS'96, LNCS 1046, pp. 453–464.

    Google Scholar 

  8. F. Harary. Graph Theory. Addison-Wesley, Reading, Massachusetts, 1979.

    Google Scholar 

  9. J. Hopcroft and R. Karp. An n 5/2 algorithm for maximum matching in bipartite graphs. SIAM J.Comput. 2:4 (1973), pp. 225–231.

    Google Scholar 

  10. J. van Leeuwen. Graph Algorithms. Handbook of Theoretical Computer Science A, North Holland, Amsterdam 1990, pp. 527–631.

    Google Scholar 

  11. A. Lingas. Subgraph isomorphism for biconnected outerplanar graphs in cubic time. Theoretical Computer Science 68 (1989), pp. 295–302.

    Google Scholar 

  12. A. Lingas and M. Karpinski. Subtree Isomorphism and Bipartite Perfect Matching are Mutually NC Reducible. Tech. Rept. 856-CS, December 1986, Bonn University.

    Google Scholar 

  13. A. Lingas and M. Sysło. A Polynomial Algorithm for Subgraph Isomorphism of Two-connected Series-Parallel Graphs. Proc. ICALP'88, LNCS 317, pp. 394–409, Springer Verlag.

    Google Scholar 

  14. D. Matula. Subtree isomorphism in O(n 5/2). Annals of Discrete Mathematics 2 (1978), pp. 91–106.

    Google Scholar 

  15. J. Matoušek and R. Thomas. On the complexity of finding iso-and other morphisms for partial k-trees. Discrete Mathematics 108 (1992), pp. 343–364.

    Article  Google Scholar 

  16. A. Proskurowski, M. Sysio and P. Winter. Plane embeddings of 2-trees and biconnected partial 2-trees. To appear in SIAM J. on Discrete Mathematics, 1996.

    Google Scholar 

  17. N. Robertson and P. Seymour. Graph Minors II. Algorithmic aspects of tree-width. J. Algorithms No. 7 (1986), pp. 309–322.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Josep Diaz Maria Serna

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dessmark, A., Lingas, A., Proskurowski, A. (1996). Faster algorithms for subgraph isomorphism of κ-connected partial κ-trees. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_78

Download citation

  • DOI: https://doi.org/10.1007/3-540-61680-2_78

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61680-1

  • Online ISBN: 978-3-540-70667-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics