Skip to main content
SpringerLink
Log in

Myhill-Nerode Methods for Hypergraphs

  • Conference paper
Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

Included in the following conference series:

Abstract

We introduce a method of applying Myhill-Nerode methods from formal language theory to hypergraphs and show how this method can be used to obtain the following parameterized complexity results.

  • Hypergraph Cutwidth (deciding whether a hypergraph on n vertices has cutwidth at most k) is linear-time solvable for constant k.

  • For hypergraphs of constant incidence treewidth (treewidth of the incidence graph), Hypertree Width and variants cannot be solved by simple finite tree automata. The proof leads us to conjecture that Hypertree Width is W[1]-hard for this parameter.

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. Abrahamson, K.R., Fellows, M.R.: Finite automata, bounded treewidth, and well-quasiordering. In: Graph Structure Theory. Contemporary Mathematics, vol. 147, pp. 539–564. American Mathematical Society (1991)

    Google Scholar 

  2. van Bevern, R., Fellows, M.R., Gaspers, S., Rosamond, F.A.: Myhill-nerode methods for hypergraphs (2013), arxiv:1211.1299v3 (cs.DM)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Bodlaender, H.L., Fellows, M.R., Thilikos, D.M.: Derivation of algorithms for cutwidth and related graph layout parameters. J. Comput. Syst. Sci. 75(4), 231–244 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cahoon, J., Sahni, S.: Exact algorithms for special cases of the board permutation problem. In: Proceedings of the 21st Annual Allerton Conference on Communication, Control, and Computing, pp. 246–255 (1983)

    Google Scholar 

  6. Diestel, R.: Graph Theory, 4th edn. Graduate Texts in Mathematics, vol. 173. Springer, New York (2010)

    Book  Google Scholar 

  7. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)

    Google Scholar 

  8. Fellows, M.R., Langston, M.A.: An analogue of the Myhill-Nerode Theorem and its use in computing finite-basis characterizations (extended abstract). In: Proc. 30th FOCS, pp. 520–525. IEEE Computer Society (1989)

    Google Scholar 

  9. Fellows, M.R., Langston, M.A.: On well-partial-order theory and its application to combinatorial problems of VLSI design. SIAM J. Discrete Math. 5(1), 117–126 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fellows, M.R., Langston, M.A.: On search, decision, and the efficiency of polynomial-time algorithms. J. Comput. Syst. Sci. 49(3), 769–779 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gavril, F.: Some NP-complete problems on graphs. In: Proc. 1977 Conf. on Inf. Sc. and Syst., pp. 91–95. Johns Hopkins Univ. (1977)

    Google Scholar 

  12. Gottlob, G., Grohe, M., Musliu, N., Samer, M., Scarcello, F.: Hypertree decompositions: Structure, algorithms, and applications. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 1–15. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Gottlob, G., Miklós, Z., Schwentick, T.: Generalized hypertree decompositions: NP-hardness and tractable variants. J. ACM 56(6) (2009)

    Google Scholar 

  14. Kolaitis, P.G., Vardi, M.Y.: Conjunctive-query containment and constraint satisfaction. J. Comput. Sci. 61(2), 302–332 (2000)

    MathSciNet  MATH  Google Scholar 

  15. Marx, D.: Approximating fractional hypertree width. ACM Transactions on Algorithms 6(2), 1–29 (2010)

    Article  MathSciNet  Google Scholar 

  16. Miller, Z., Sudborough, I.H.: A polynomial algorithm for recognizing bounded cutwidth in hypergraphs. Mathematical Systems Theory 24(1), 11–40 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nagamochi, H.: Linear layouts in submodular systems. In: Chao, K.-M., Hsu, T.-s., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 475–484. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Samer, M., Szeider, S.: Constraint satisfaction with bounded treewidth revisited. J. Comput. Sci. 76(2), 103–114 (2010)

    MathSciNet  MATH  Google Scholar 

  19. Thilikos, D.M., Serna, M.J., Bodlaender, H.L.: Cutwidth I: A linear time fixed parameter algorithm. J. Algorithms 56(1), 1–24 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Germany

    René van Bevern

  2. School of Engineering and IT, Charles Darwin University, Darwin, Australia

    Michael R. Fellows & Frances A. Rosamond

  3. NICTA, The University of New South Wales, Sydney, Australia

    Serge Gaspers

Authors
  1. René van Bevern
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael R. Fellows
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Serge Gaspers
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Frances A. Rosamond
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Bevern, R., Fellows, M.R., Gaspers, S., Rosamond, F.A. (2013). Myhill-Nerode Methods for Hypergraphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-45030-3_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation