Skip to main content
SpringerLink
Log in

Connected Feedback VertexSet on AT-Free Graphs

  • Conference paper
  • First Online:
Combinatorial Algorithms (IWOCA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13889))

Included in the following conference series:

  • 379 Accesses

Abstract

A connected feedback vertex set of a graph is a connected subgraph of the graph whose removal makes the graph cycle free. In this paper, we give an approximation algorithm that computes a connected feedback vertex set of size \((1.9091OPT+6)\) on \(2-\)connected AT-free graphs with running time \(O(n^8m^2)\). Also, we give another approximation algorithm that computes a connected feedback vertex set of size \((2.9091OPT+6)\) on the same graph class with more efficient running time \(O(min\{m(log(n)),n^2\})\).

The second author is a doctoral student at Ramakrishna Mission Vivekananda Educational and Research Institute (RKMVERI) and Institute of Advancing Intelligence (IAI), TCG CREST.

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 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
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

References

  1. Abrishami, T., Chudnovsky, M., Pilipczuk, M., Rzążewski, P., Seymour, P.: Induced subgraphs of bounded treewidth and the container method. In: Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1948–1964. SIAM (2021)

    Google Scholar 

  2. Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Discret. Math. 12(3), 289–297 (1999)

    Article  MathSciNet  Google Scholar 

  3. Balakrishnan, H., Rajaraman, A., Rangan, C.P.: Connected domination and Steiner set on asteroidal triple-free graphs. In: Dehne, F., Sack, J.-R., Santoro, N., Whitesides, S. (eds.) WADS 1993. LNCS, vol. 709, pp. 131–141. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57155-8_242

    Chapter  Google Scholar 

  4. Belmonte, R., van’t Hof, P., Kamiński, M., Paulusma, D.: The price of connectivity for feedback vertex set. Discret. Appl. Math. 217, 132–143 (2017)

    Google Scholar 

  5. Broersma, H., Kloks, T., Kratsch, D., Müller, H.: Independent sets in asteroidal triple-free graphs. SIAM J. Discret. Math. 12(2), 276–287 (1999)

    Article  MathSciNet  Google Scholar 

  6. Chiarelli, N., Hartinger, T.R., Johnson, M., Milanič, M., Paulusma, D.: Minimum connected transversals in graphs: new hardness results and tractable cases using the price of connectivity. Theor. Comput. Sci. 705, 75–83 (2018)

    Article  MathSciNet  Google Scholar 

  7. Corneil, D.G., Olariu, S., Stewart, L.: Computing a dominating pair in an asteroidal triple-free graph in linear time. In: Akl, S.G., Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 358–368. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60220-8_76

    Chapter  Google Scholar 

  8. Corneil, D.G., Olariu, S., Stewart, L.: Asteroidal triple-free graphs. SIAM J. Discret. Math. 10(3), 399–430 (1997)

    Article  MathSciNet  Google Scholar 

  9. Dabrowski, K.K., Feghali, C., Johnson, M., Paesani, G., Paulusma, D., Rzążewski, P.: On cycle transversals and their connected variants in the absence of a small linear forest. Algorithmica 82(10), 2841–2866 (2020)

    Article  MathSciNet  Google Scholar 

  10. Daniel Liang, Y., Chang, M.-S.: Minimum feedback vertex sets in cocomparability graphs and convex bipartite graphs. Acta Informatica 34(5) (1997)

    Google Scholar 

  11. Grigoriev, A., Sitters, R.: Connected feedback vertex set in planar graphs. In: Paul, C., Habib, M. (eds.) WG 2009. LNCS, vol. 5911, pp. 143–153. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11409-0_13

    Chapter  Google Scholar 

  12. Gross, J.L., Yellen, J., Anderson, M.: Graph Theory and its Applications. Chapman and Hall/CRC (2018)

    Google Scholar 

  13. Hartmanis, J.: Computers and intractability: a guide to the theory of np-completeness (Michael R. Garey and David S. Johnson). SIAM Rev. 24(1), 90 (1982)

    Google Scholar 

  14. Kratsch, D.: Domination and total domination on asteroidal triple-free graphs. Discret. Appl. Math. 99(1–3), 111–123 (2000)

    Article  MathSciNet  Google Scholar 

  15. Kratsch, D., Müller, H., Todinca, I.: Feedback vertex set on at-free graphs. Discret. Appl. Math. 156(10), 1936–1947 (2008)

    Article  MathSciNet  Google Scholar 

  16. Daniel Liang, Y.: On the feedback vertex set problem in permutation graphs. Inf. Process. Lett. 52(3), 123–129 (1994)

    Article  MathSciNet  Google Scholar 

  17. Lu, C.L., Tang, C.Y.: A linear-time algorithm for the weighted feedback vertex problem on interval graphs. Inf. Process. Lett. 61(2), 107–111 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India

    Joydeep Mukherjee & Tamojit Saha

  2. Institute of Advancing Intelligence, TCG CREST, Kolkata, India

    Tamojit Saha

Authors
  1. Joydeep Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tamojit Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tamojit Saha .

Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Sun-Yuan Hsieh

  2. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  3. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mukherjee, J., Saha, T. (2023). Connected Feedback VertexSet on AT-Free Graphs. In: Hsieh, SY., Hung, LJ., Lee, CW. (eds) Combinatorial Algorithms. IWOCA 2023. Lecture Notes in Computer Science, vol 13889. Springer, Cham. https://doi.org/10.1007/978-3-031-34347-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-34347-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34346-9

  • Online ISBN: 978-3-031-34347-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation