Skip to main content

Logspace and FPT Algorithms for Graph Isomorphism for Subclasses of Bounded Tree-Width Graphs

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8973)

Abstract

We give a deterministic logspace algorithm for the graph isomorphism problem for graphs with bounded tree-depth. We also show that the graph isomorphism problem is fixed parameter tractable for a related parameterized graph class where the graph parameter is the length of the longest cycle.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-15612-5_30
  • Chapter length: 6 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-15612-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arvind, V., Das, B., Köbler, J.: A logspace algorithm for partial 2-tree canonization. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) CSR 2008. LNCS, vol. 5010, pp. 40–51. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  2. Arvind, V., Das, B., Köbler, J., Kuhnert, S.: The isomorphism problem for k-trees is complete for logspace. Information and Computation 217, 1–11 (2012)

    MATH  MathSciNet  CrossRef  Google Scholar 

  3. Bouland, A., Dawar, A., Kopczyński, E.: On tractable parameterizations of graph isomorphism. In: Thilikos, D.M., Woeginger, G.J. (eds.) IPEC 2012. LNCS, vol. 7535, pp. 218–230. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  4. Das, B., Torán, J., Wagner, F.: Restricted space algorithms for isomorphism on bounded treewidth graphs. Information and Computation 217, 71–83 (2012)

    MATH  MathSciNet  CrossRef  Google Scholar 

  5. Datta, S., Limaye, N., Nimbhorkar, P., Thierauf, T., Wagner, F.: Planar graph isomorphism is in log-space. In: Proceedings of 24th Annual IEEE Conference on Computational Complexity, pp. 203–214. IEEE (2009)

    Google Scholar 

  6. Datta, S., Nimbhorkar, P., Thierauf, T., Wagner, F.: Graph isomorphism for K3,3-free and K5-free graphs is in log-space. In: LIPIcs-Leibniz International Proceedings in Informatics. vol. 4. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2009)

    Google Scholar 

  7. Diestel, R.: Graph Theory Graduate Texts in Mathematics, vol. 173. Springer, GmbH & Company KG, Berlin and Heidelberg (2000)

    Google Scholar 

  8. Elberfeld, M., Jakoby, A., Tantau, T.: Algorithmic meta theorems for circuit classes of constant and logarithmic depth. In: Symposium on Theoretical Aspects of Computer Science, vol. 14, pp. 66–77 (2012)

    Google Scholar 

  9. Evdokimov, S., Ponomarenko, I.: Isomorphism of coloured graphs with slowly increasing multiplicity of jordan blocks. Combinatorica 19(3), 321–333 (1999)

    MATH  MathSciNet  CrossRef  Google Scholar 

  10. Kratsch, S., Schweitzer, P.: Isomorphism for graphs of bounded feedback vertex set number. In: Kaplan, H. (ed.) SWAT 2010. LNCS, vol. 6139, pp. 81–92. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  11. Lindell, S.: A logspace algorithm for tree canonization. In: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pp. 400–404. ACM (1992)

    Google Scholar 

  12. Lokshtanov, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Fixed-parameter tractable canonization and isomorphism test for graphs of bounded treewidth. In: FOCS (2014), http://arxiv.org/abs/1404.0818

  13. Nešetřil, J., De Mendez, P.O.: Sparsity: Graphs, Structures, and Algorithms, vol. 28. Springer (2012)

    Google Scholar 

  14. Nešetřil, J., de Mendez, P.O.: Tree-depth, subgraph coloring and homomorphism bounds. European Journal of Combinatorics 27(6), 1022–1041 (2006)

    MATH  MathSciNet  CrossRef  Google Scholar 

  15. Reingold, O.: Undirected connectivity in log-space. J. ACM 55(4), 17:1–17:24 (2008)

    Google Scholar 

  16. Yamazaki, K., Bodlaender, H.L., de Fluiter, B., Thilikos, D.M.: Isomorphism for graphs of bounded distance width. Algorithmica 24(2), 105–127 (1999)

    MATH  MathSciNet  CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Das, B., Enduri, M.K., Reddy, I.V. (2015). Logspace and FPT Algorithms for Graph Isomorphism for Subclasses of Bounded Tree-Width Graphs. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15612-5_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15611-8

  • Online ISBN: 978-3-319-15612-5

  • eBook Packages: Computer ScienceComputer Science (R0)