Skip to main content

Fast Quasi-Threshold Editing

  • Conference paper
  • First Online:
Algorithms - ESA 2015

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

  • 2345 Accesses

Abstract

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with a minimum number of edge insertions and deletions. Given a graph it computes a quasi-threshold graph which is close in terms of edit count, but not necessarily closest as this edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM performs well in practice and is the first heuristic that is able to scale to large real-world graphs in practice. As a side result we further present a simple linear-time algorithm for the quasi-threshold recognition problem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Bader, D.A., Meyerhenke, H., Sanders, P., Wagner, D.: Graph Partitioning and Graph Clustering: 10th DIMACS Implementation Challenge, vol. 588. American Mathematical Society (2013)

    Google Scholar 

  2. Blondel, V., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment 2008(10) (2008)

    Google Scholar 

  3. Boldi, P., Codenotti, B., Santini, M., Vigna, S.: Ubicrawler: A scalable fully distributed web crawler. Software - Practice and Experience 34(8), 711–726 (2004)

    Article  Google Scholar 

  4. Boldi, P., Rosa, M., Santini, M., Vigna, S.: Layered label propagation: A multiresolution coordinate-free ordering for compressing social networks. In: Proceedings of the 20th International Conference on World Wide Web (WWW 2011), pp. 587–596. ACM Press (2011)

    Google Scholar 

  5. Boldi, P., Vigna, S.: The WebGraph framework I: Compression techniques. In: Proceedings of the 13th International Conference on World Wide Web (WWW 2004), pp. 595–602. ACM Press (2004)

    Google Scholar 

  6. Brandes, U., Hamann, M., Strasser, B., Wagner, D.: Fast quasi-threshold editing (2015), http://arxiv.org/abs/1504.07379

  7. 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 

  8. Chiba, N., Nishizeki, T.: Arboricity and subgraph listing algorithms. SIAM Journal on Computing 14(1), 210–223 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chu, F.P.M.: A simple linear time certifying lbfs-based algorithm for recognizing trivially perfect graphs and their complements. Information Processing Letters 107(1), 7–12 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Drange, P.G., Dregi, M.S., Lokshtanov, D., Sullivan, B.D.: On the threshold of intractability. In: Proceedings of the 23rd Annual European Symposium on Algorithms (ESA 2015). LNCS. Springer (2015)

    Google Scholar 

  11. Drange, P.G., Pilipczuk, M.: A polynomial kernel for trivially perfect editing. In: Proceedings of the 23rd Annual European Symposium on Algorithms (ESA 2015). LNCS. Springer (2015)

    Google Scholar 

  12. Görke, R., Kappes, A., Wagner, D.: Experiments on density-constrained graph clustering. ACM Journal of Experimental Algorithmics 19, 1.6:1.1–1.6:1.31 (2014)

    Google Scholar 

  13. Leskovec, J., Krevl, A.: Snap datasets: Stanford large network dataset collection (June 2014), http://snap.stanford.edu/data

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

    Google Scholar 

  15. Ortmann, M., Brandes, U.: Triangle listing algorithms: Back from the diversion. In: Proceedings of the 16th Meeting on Algorithm Engineering and Experiments (ALENEX 2014), pp. 1–8. SIAM (2014)

    Google Scholar 

  16. Rotta, R., Noack, A.: Multilevel local search algorithms for modularity clustering. ACM Journal of Experimental Algorithmics 16, 2.3:2.1–2.3:2.27 (2011)

    Google Scholar 

  17. Staudt, C., Sazonovs, A., Meyerhenke, H.: Networkit: An interactive tool suite for high-performance network analysis (2014), http://arxiv.org/abs/1403.3005

  18. Traud, A.L., Mucha, P.J., Porter, M.A.: Social structure of facebook networks. Physica A: Statistical Mechanics and its Applications 391(16), 4165–4180 (2012)

    Article  Google Scholar 

  19. Wolk, E.S.: A note on “the comparability graph of a tree”. Proceedings of the American Mathematical Society 16(1), 17–20 (1965)

    MathSciNet  MATH  Google Scholar 

  20. Yan, J.H., Chen, J.J., Chang, G.J.: Quasi-threshold graphs. Discrete Applied Mathematics 69(3), 247–255 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ulrik Brandes .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brandes, U., Hamann, M., Strasser, B., Wagner, D. (2015). Fast Quasi-Threshold 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_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48350-3_22

  • 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