Skip to main content
SpringerLink
Log in

An Effective Branching Strategy for Some Parameterized Edge Modification Problems with Multiple Forbidden Induced Subgraphs

  • Conference paper
Computing and Combinatorics (COCOON 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7936))

Included in the following conference series:

Abstract

Branching on forbidden induced subgraphs is a genetic strategy to obtain parameterized algorithms for many edge modification problems. For such a problem in which the graph property is defined by multiple forbidden induced subgraphs, branching process is trivially performed on each subgraph. Thus, the size of the resulting search tree is dominated by the size of the largest forbidden subgraph. In this paper, we present a simple strategy for deriving significantly improved branching rules for dealing with multiple forbidden subgraphs by edge modifications. The basic idea hereby is that while constructing branching rules for the largest forbidden subgraph, we sufficiently take into account the structural relationship between it and other forbidden subgraphs. By applying this strategy, we obtain improved parameterized algorithms for edge modification problems for several graph properties such as proper interval, 3-leaf power, threshold and co-trivially perfect graphs.

This research was supported in part by the National Natural Science Foundation of China under Grant No.61070224, No.61232001, and No.61128006, the China Postdoctoral Science Foundation funded project under Grant No. 2012M521551, and the DFG Cluster of Excellence “Multimodal Computing and Interaction (MMCI)”.

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.

References

  1. Bessy, S., Paul, C., Perez, A.: Polynomial Kernels for 3-Leaf Power Graph Modification Problems. Discrete Applied Mathematics 158(16), 1732–1744 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bessy, S., Perez, A.: Polynomial kernels for proper interval completion and related problems. In: Owe, O., Steffen, M., Telle, J.A. (eds.) FCT 2011. LNCS, vol. 6914, pp. 229–239. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Brandstäda, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications (1999)

    Google Scholar 

  4. Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–196 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dom, M., Guo, J., Hüffner, F., Niedermeier, R.: Error compensation in leaf power problems. Algorithmica 44(4), 363–381 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Guo, J., Hüffner, F., Komusiewicz, C., Zhang, Y.: Improved algorithms for bicluster editing. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 445–456. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. 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 

  9. Kaplan, H., Shamir, R., Tarjan, R.E.: Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM J. Comput. 28(5), 1906–1922 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu, Y., Wang, J., Guo, J., Chen, J.: Cograph editing: Complexity and parameterized algorithms. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 110–121. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Nastos, J., Gao, Y.: A novel branching strategy for parameterized graph modification problems. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 332–346. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter tractable algorithms. Information Processing Letters 73, 125–129 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sharan, R.: Graph modification problems and their applications to genomic research. PhD Thesis, Tel-Aviv University (2002)

    Google Scholar 

  14. Villanger, Y.: Proper interval vertex deletion. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 228–238. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Wegner, G.: Eigenschaften der Nerven homologisch-einfacher Familien im R n. PhD thesis, Universität Göttingen (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, P.R. China

    Yunlong Liu, Jianxin Wang, Chao Xu & Jianer Chen

  2. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China), Hunan Normal University, Changsha, 410081, P.R. China

    Yunlong Liu

  3. Universität des Saarlandes, Campus E 1.7, D-66123, Saarbrücken, Germany

    Jiong Guo

  4. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Jianer Chen

Authors
  1. Yunlong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianxin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jianer Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

  2. College of Computer Science and Technology, Zhejiang University, 310027, Hangzhou, China

    Guochuan Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liu, Y., Wang, J., Xu, C., Guo, J., Chen, J. (2013). An Effective Branching Strategy for Some Parameterized Edge Modification Problems with Multiple Forbidden Induced Subgraphs. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38768-5_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38767-8

  • Online ISBN: 978-3-642-38768-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation