Skip to main content
SpringerLink
Log in

Minimal Interval Completions

  • Conference paper
Algorithms – ESA 2005 (ESA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

Included in the following conference series:

Abstract

We study the problem of adding edges to an arbitrary graph so that the resulting graph is an interval graph. Our objective is to add an inclusion minimal set of edges, which means that no proper subset of the added edges can result in an interval graph when added to the original graph. We give a polynomial time algorithm to obtain a minimal interval completion of an arbitrary graph, thereby resolving the complexity of this problem.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Berry, A., Heggernes, P., Villanger, Y.: A vertex incremental approach for dynamically maintaining chordal graphs. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 47–57. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Bouchitté, V., Todinca, I.: Treewidth and minimum fill-in: grouping the minimal separators. SIAM J. on Computing 31(1), 212–232 (2001)

    Article  MATH  Google Scholar 

  3. Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co., New York (1978)

    Google Scholar 

  4. Gilmore, P.C., Hoffman, A.J.: A characterization of comparability graphs and of interval graphs. Canadian J. Math. 16, 539–548 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  5. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)

    MATH  Google Scholar 

  6. Goldberg, P.W., Golumbic, M.C., Kaplan, H., Shamir, R.: Four strikes against physical mapping of DNA. J. Comput. Bio. 2(1), 139–152 (1995)

    Article  Google Scholar 

  7. Gustedt, J.: On the pathwidth of chordal graphs. Discrete Applied Mathematics 45(3), 233–248 (2003)

    Article  MathSciNet  Google Scholar 

  8. Heggernes, P.: Minimal triangulations of graphs: A survey. To appear Discrete Math.

    Google Scholar 

  9. Heggernes, P., Suchan, K., Todinca, I., Villanger, Y.: Minimal interval completions. Technical Report RR2005-04, LIFO - University of Orléans (2005), http://www.univ-orleans.fr/SCIENCES/LIFO/prodsci/rapports/RR2005.htm.en

  10. Kloks, T., Kratsch, D., Spinrad, J.: On treewidth and minimum fill-in of asteroidal triple-free graphs. Theor. Comput. Sci. 175, 309–335 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lekkerkerker, C.G., Boland, J.C.: Representation of a finite graph by a set of intervals on the real line. Fund. Math. 51, 45–64 (1962)

    MATH  MathSciNet  Google Scholar 

  12. Parra, A., Scheffler, P.: Characterizations and algorithmic applications of chordal graph embeddings. Disc. Appl. Math. 79, 171–188 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Rose, D., Tarjan, R.E., Lueker, G.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 146–160 (1976)

    Article  MathSciNet  Google Scholar 

  14. Yannakakis, M.: Computing the minimum fill-in is NP-complete. SIAM J. Alg. Disc. Meth. 2, 77–79 (1981)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Pinar Heggernes & Yngve Villanger

  2. LIFO, Université d’Orleans, PB 6759, F-45067 Cedex 2, Orleans, France

    Karol Suchan & Ioan Todinca

Authors
  1. Pinar Heggernes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karol Suchan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ioan Todinca
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yngve Villanger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. BRICS, MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Gerth Stølting Brodal

  2. University of Rome “La Sapienza”, Rome, Italy

    Stefano Leonardi

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Heggernes, P., Suchan, K., Todinca, I., Villanger, Y. (2005). Minimal Interval Completions. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_37

Download citation

  • DOI: https://doi.org/10.1007/11561071_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation