Cograph Editing: Complexity and Parameterized Algorithms

  • Yunlong Liu
  • Jianxin Wang
  • Jiong Guo
  • Jianer Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6842)


Cograph Editing is to find for a given graph G = (V,E) a set of at most k edge additions and deletions that transform G into a cograph. The computational complexity of this problem was open in the past. In this paper, we show that this problem is NP-hard, and present a parameterized algorithm based on a refined search tree technique with a running time of O(4.612k + |V|4.5)), which improves the trivial algorithm of running time O(6k + |V|4.5).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Asdre, K., Nikolopoulos, S.D., Papadopoulos, C.: An optimal parallel solution for the path cover problem on P 4-sparse graphs. Journal of Parallel and Distributed Computing 67(1), 63–76 (2007)CrossRefMATHGoogle Scholar
  2. 2.
    Burzyn, P., Bonomo, F., Durán, G.: NP-completeness results for edge modification problems. Discrete Applied Mathematics 154(13), 1824–1844 (2006)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–196 (1996)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Chen, J., Meng, J.: A 2k kernel for the cluster editing problem. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 459–468. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Corneil, G., Perl, Y., Stewart, L.K.: A linear recognition algorithm for cographs. SIAM Journal on Computing 14(4), 926–934 (1985)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    El-Mallah, E.S., Colbourn, C.J.: The complexity of some edge deletion problems. IEEE Transactions on Circuits and Systems 35(3), 354–362 (1988)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Exact algorithms for clique generation. Theory of Computing Systems 38(4), 373–392 (2005)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Guillemot, S., Paul, C., Perez, A.: On the (Non-)existence of polynomial kernels for pl-free edge modification problems. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 147–157. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Hoàng, C.T.: Perfect graphs. PhD Thesis, School of Computer Science. McGill University, Montreal (1985)Google Scholar
  12. 12.
    Jamison, B., Olariu, S.: Recognizing P 4-sparse graphs in linear time. SIAM Journal on Computing 21(2), 381–406 (1992)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Mancini, F.: Graph Modification Problems Related to Graph Classes. PhD Thesis, University of Bergen (2008)Google Scholar
  14. 14.
    McConnell, R.M., Spinrad, J.: Modular decomposition and transitive orientation. Discrete Mathematics 201(1-3), 189–241 (1999)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Applied Mathematics 113(1), 109–128 (2001)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter tractable algorithms. Information Processing Letters 73, 125–129 (2000)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Protti, F., Silva, M.D., Szwarcfiter, J.L.: Applying Modular Decomposition to Parameterized Cluster Editing Problems. Theory of Computing Systems 44, 91–104 (2009)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Seinsche, D.: On a property of the class of n-colorable graphs. Journal of Combinatorial Theory, Series B 16, 191–193 (1974)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yunlong Liu
    • 1
  • Jianxin Wang
    • 2
  • Jiong Guo
    • 3
  • Jianer Chen
    • 2
    • 4
  1. 1.School of Mathematics and Computer ScienceHunan Normal UniversityChangshaP.R. China
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaP.R. China
  3. 3.Universität des Saarlandes, Campus E 1.7SaarbrückenGermany
  4. 4.Department of Computer Science and EngineeringTexas A&M University, College StationUSA

Personalised recommendations