Skip to main content
SpringerLink
Log in

Computing Tree-Depth Faster Than 2n

  • Conference paper
Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

Included in the following conference series:

Abstract

A connected graph has tree-depth at most k if it is a subgraph of the closure of a rooted tree whose height is at most k. We give an algorithm which for a given n-vertex graph G, in time \(\mathcal{O}^*(1.9602^n)\) computes the tree-depth of G. Our algorithm is based on combinatorial results revealing the structure of minimal rooted trees whose closures contain G.

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.

Similar content being viewed by others

References

  1. Björklund, A.: Determinant sums for undirected hamiltonicity. In: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010), pp. 173–182. IEEE (2010)

    Google Scholar 

  2. Bodlaender, H.L., Deogun, J.S., Jansen, K., Kloks, T., Kratsch, D., Müller, H., Tuza, Z.: Rankings of graphs. SIAM J. Discrete Math. 11(1), 168–181 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bodlaender, H.L., Fomin, F.V., Koster, A.M.C.A., Kratsch, D., Thilikos, D.M.: A note on exact algorithms for vertex ordering problems on graphs. Theory Comput. Syst. 50(3), 420–432 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bodlaender, H.L., Gilbert, J.R., Hafsteinsson, H., Kloks, T.: Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. J. Algorithms 18(2), 238–255 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cygan, M., Lokshtanov, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: On cutwidth parameterized by vertex cover. Algorithmica, 1–14 (2012)

    Google Scholar 

  6. Deogun, J.S., Kloks, T., Kratsch, D., Müller, H.: On the vertex ranking problem for trapezoid, circular-arc and other graphs. Discrete Applied Mathematics 98(1-2), 39–63 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fomin, F.V., Kratsch, D., Todinca, I., Villanger, Y.: Exact algorithms for treewidth and minimum fill-in. SIAM J. Comput. 38(3), 1058–1079 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fomin, F.V., Villanger, Y.: Treewidth computation and extremal combinatorics. Combinatorica 32(3), 289–308 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. Journal of SIAM 10, 196–210 (1962)

    MathSciNet  MATH  Google Scholar 

  10. Katchalski, M., McCuaig, W., Seager, S.M.: Ordered colourings. Discrete Mathematics 142(1-3), 141–154 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kitsunai, K., Kobayashi, Y., Komuro, K., Tamaki, H., Tano, T.: Computing directed pathwidth in O(1.89n) time. In: Thilikos, D.M., Woeginger, G.J. (eds.) IPEC 2012. LNCS, vol. 7535, pp. 182–193. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Kloks, T., Müller, H., Wong, C.K.: Vertex ranking of asteroidal triple-free graphs. Inf. Process. Lett. 68(4), 201–206 (1998)

    Article  Google Scholar 

  13. Nešetřil, J., de Mendez, P.O.: Tree-depth, subgraph coloring and homomorphism bounds. Eur. J. Comb. 27(6), 1022–1041 (2006)

    Article  MATH  Google Scholar 

  14. Nešetřil, J., de Mendez, P.O.: Grad and classes with bounded expansion I. Decompositions. Eur. J. Comb. 29(3), 760–776 (2008)

    Article  MATH  Google Scholar 

  15. Nešetřil, J., de Mendez, P.O.: Grad and classes with bounded expansion II. Algorithmic aspects. Eur. J. Comb. 29(3), 777–791 (2008)

    Article  MATH  Google Scholar 

  16. Nešetřil, J., de Mendez, P.O.: Grad and classes with bounded expansion III. Restricted graph homomorphism dualities. Eur. J. Comb. 29(4), 1012–1024 (2008)

    Article  MATH  Google Scholar 

  17. Nešetřil, J., de Mendez, P.O.: Sparsity - Graphs, Structures, and Algorithms. Algorithms and combinatorics, vol. 28. Springer (2012)

    Google Scholar 

  18. Robertson, N., Seymour, P.D.: Graph Minors. XIII. The Disjoint Paths Problem. J. Comb. Theory, Ser. B 63(1), 65–110 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Robertson, N., Seymour, P.D.: Graph Minors. XX. Wagner’s conjecture. J. Comb. Theory, Ser. B 92(2), 325–357 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Schäffer, A.A.: Optimal Node Ranking of Trees in Linear Time. Inf. Process. Lett. 33(2), 91–96 (1989)

    Article  MATH  Google Scholar 

  21. Suchan, K., Villanger, Y.: Computing pathwidth faster than 2n. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 324–335. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, P.O. Box 7803, 5020, Bergen, Norway

    Fedor V. Fomin, Archontia C. Giannopoulou & Michał Pilipczuk

Authors
  1. Fedor V. Fomin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Archontia C. Giannopoulou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michał Pilipczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Fomin, F.V., Giannopoulou, A.C., Pilipczuk, M. (2013). Computing Tree-Depth Faster Than 2n . In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03898-8_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation