Skip to main content
SpringerLink
Log in

Isomorphism for Graphs of Bounded Feedback Vertex Set Number

  • Conference paper
Algorithm Theory - SWAT 2010 (SWAT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6139))

Included in the following conference series:

Abstract

This paper presents an \({\mathcal O}(n^2)\) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixed-parameter tractable with respect to the feedback vertex set number. Central to the algorithm is a new technique consisting of an application of reduction rules that produce an isomorphism-invariant outcome, interleaved with the creation of increasingly large partial isomorphisms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arvind, V., Das, B., Köbler, J., Toda, S.: Colored hypergraph isomorphism is fixed parameter tractable. ECCC 16(093) (2009)

    Google Scholar 

  2. Babai, L.: Moderately exponential bound for graph isomorphism. In: FCT, pp. 34–50. Springer, Heidelberg (1981)

    Google Scholar 

  3. Babai, L., Grigoryev, D.Y., Mount, D.M.: Isomorphism of graphs with bounded eigenvalue multiplicity. In: STOC, pp. 310–324. ACM, New York (1982)

    Google Scholar 

  4. Babai, L., Luks, E.M.: Canonical labeling of graphs. In: STOC, pp. 171–183. ACM, New York (1983)

    Google Scholar 

  5. Bodlaender, H.L.: Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees. Journal of Algorithms 11(4), 631–643 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25(6), 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–176 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, J., Fomin, F.V., Liu, Y., Lu, S., Villanger, Y.: Improved algorithms for feedback vertex set problems. Journal of Computer and System Sciences 74(7), 1188–1198 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Downey, R.G., Fellows, M.R.: Parameterized Complexity (Monographs in Computer Science). Springer, Heidelberg (1998)

    Google Scholar 

  10. Enciso, R., Fellows, M.R., Guo, J., Kanj, I.A., Rosamond, F.A., Suchý, O.: What makes equitable connected partition easy. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 122–133. Springer, Heidelberg (2009)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Filotti, I.S., Mayer, J.N.: A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus. In: STOC, pp. 236–243. ACM, New York (1980)

    Google Scholar 

  13. Furst, M.L., Hopcroft, J.E., Luks, E.M.: Polynomial-time algorithms for permutation groups. In: FOCS, pp. 36–41. IEEE, Los Alamitos (1980)

    Google Scholar 

  14. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  15. Hopcroft, J.E., Wong, J.K.: Linear time algorithm for isomorphism of planar graphs. In: STOC, pp. 310–324. ACM, New York (1974)

    Google Scholar 

  16. Kawarabayashi, K., Mohar, B., Reed, B.A.: A simpler linear time algorithm for embedding graphs into an arbitrary surface and the genus of graphs of bounded tree-width. In: FOCS, pp. 771–780. IEEE, Los Alamitos (2008)

    Google Scholar 

  17. Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM Journal on Computing 6(2), 323–350 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  18. Luks, E.M.: Isomorphism of graphs of bounded valence can be tested in polynomial time. Journal of Computer and System Sciences 25(1), 42–65 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  19. Marx, D.: Chordal deletion is fixed-parameter tractable. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 37–48. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Miller, G.L.: Isomorphism testing for graphs of bounded genus. In: STOC, pp. 225–235. ACM, New York (1980)

    Google Scholar 

  21. Ponomarenko, I.N.: The isomorphism problem for classes of graphs closed under contraction. Journal of Mathematical Sciences 55(2), 1621–1643 (1991)

    Article  MathSciNet  Google Scholar 

  22. Raman, V., Saurabh, S., Subramanian, C.R.: Faster fixed parameter tractable algorithms for finding feedback vertex sets. ACM Transactions on Algorithms 2(3), 403–415 (2006)

    Article  MathSciNet  Google Scholar 

  23. Schöning, U.: Graph isomorphism is in the low hierarchy. Journal of Computer and System Sciences 37(3), 312–323 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  24. Tarjan, R.E.: A V 2 algorithm for determining isomorphism of planar graphs. Information Processing Letters 1(1), 32–34 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  25. Thomassé, S.: A quadratic kernel for feedback vertex set. In: SODA, pp. 115–119. SIAM, Philadelphia (2009)

    Google Scholar 

  26. Toda, S.: Computing automorphism groups of chordal graphs whose simplicial components are of small size. IEICE Transactions 89-D(8), 2388–2401 (2006)

    Google Scholar 

  27. Uehara, R., Toda, S., Nagoya, T.: Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs. Discrete Applied Mathematics 145(3), 479–482 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, 66123, Saarbrücken, Germany

    Stefan Kratsch & Pascal Schweitzer

Authors
  1. Stefan Kratsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pascal Schweitzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Haim Kaplan

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kratsch, S., Schweitzer, P. (2010). Isomorphism for Graphs of Bounded Feedback Vertex Set Number. In: Kaplan, H. (eds) Algorithm Theory - SWAT 2010. SWAT 2010. Lecture Notes in Computer Science, vol 6139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13731-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13731-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13730-3

  • Online ISBN: 978-3-642-13731-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation