Skip to main content
SpringerLink
Log in

A Polynomial Kernel for Trivially Perfect Editing

  • Conference paper
  • First Online:
Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

We give a kernel with O(k 7) vertices for Trivially Perfect Editing, the problem of adding or removing at most k edges in order to make a given graph trivially perfect. This answers in affirmative an open question posed by Nastos and Gao (Social Networks, 35(3):439–450, 2013) and by Liu, Wang, and Guo (Tsinghua Science and Technology, 19(4):346–357, 2014). Using our technique one can also obtain kernels of the same size for the related problems, Trivially Perfect Completion and Trivially Perfect Deletion.

We complement our study of Trivially Perfect Editing by proving that, contrary to Trivially Perfect Completion, it cannot be solved in time 2o(k)·n O(1) unless the Exponential Time Hypothesis fails. In this manner we complete the picture of the parameterized and kernelization complexity of the classic edge modification problems for the class of trivially perfect graphs.

Pilipczuk currently holds a post-doc position at Warsaw Center of Mathematics and Computer Science and is supported by the Polish National Science Centre grant DEC-2013/11/D/ST6/03073. This work has received funding from ERC grant n. 267959 (Drange and Pilipczuk, while the latter was affiliated with Univ. of Bergen).

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. Abu-Khzam, F.N.: Kernelization algorithms for d-hitting set problems. J. Comput. Syst. Sci. 76(7), 524–531 (2010)

    Article  MATH  Google Scholar 

  2. Burzyn, P., Bonomo, F., Durán, G.: NP-completeness results for edge modification problems. Discrete Applied Mathematics 154(13), 1824–1844 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Cai, L., Cai, Y.: Incompressibility of H-free edge modification. Algorithmica 71(3), 731–757 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cygan, M., Pilipczuk, M., Pilipczuk, M., van Leeuwen, E.J., Wrochna, M.: Polynomial kernelization for removing induced claws and diamonds. In: WG (2015)

    Google Scholar 

  6. Drange, P.G., Dregi, M.S., Lokshtanov, D., Sullivan, B.D.: On the Intractability of Threshold Editing. In: ESA (2015)

    Google Scholar 

  7. Drange, P.G., Fomin, F.V., Pilipczuk, M., Villanger, Y.: Exploring subexponential parameterized complexity of completion problems. In: STACS (2014)

    Google Scholar 

  8. Drange, P.G., Pilipczuk, M.: A Polynomial Kernel for Trivially Perfect Editing. CoRR, abs/1412.7558 (2014)

    Google Scholar 

  9. Fomin, F.V., Lokshtanov, D., Misra, N., Saurabh, S.: Planar F-deletion: Approximation, kernelization and optimal FPT algorithms. In: FOCS (2012)

    Google Scholar 

  10. Guillemot, S., Havet, F., Paul, C., Perez, A.: On the (non-)existence of polynomial kernels for P ℓ-free edge modification problems. Algorithmica 65(4), 900–926 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Guo, J.: Problem kernels for NP-complete edge deletion problems: Split and related graphs. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 915–926. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? Journal of Computer and System Sciences 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Komusiewicz, C., Uhlmann, J.: Cluster editing with locally bounded modifications. Discrete Applied Mathematics 160(15), 2259–2270 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kratsch, S., Wahlström, M.: Two edge modification problems without polynomial kernels. Discrete Optimization 10(3), 193–199 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Liu, Y., Wang, J., Guo, J.: An overview of kernelization algorithms for graph modification problems. Tsinghua Science and Technology 19(4), 346–357 (2014)

    Article  MathSciNet  Google Scholar 

  16. Nastos, J., Gao, Y.: Familial groups in social networks. Social Networks 35(3), 439–450 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Informatics, Univ. Bergen, Bergen, Norway

    Pål Grønås Drange

  2. Inst. Informatics, Univ. Warsaw, Warsaw, Poland

    Michał Pilipczuk

Authors
  1. Pål Grønås Drange
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michał Pilipczuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pål Grønås Drange .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Drange, P.G., Pilipczuk, M. (2015). A Polynomial Kernel for Trivially Perfect Editing. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48350-3_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation