Partitioning into Colorful Components by Minimum Edge Deletions

  • Sharon Bruckner
  • Falk Hüffner
  • Christian Komusiewicz
  • Rolf Niedermeier
  • Sven Thiel
  • Johannes Uhlmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


The NP-hard Colorful Components problem is, given a vertex-colored graph, to delete a minimum number of edges such that no connected component contains two vertices of the same color. It has applications in multiple sequence alignment and in multiple network alignment where the colors correspond to species. We initiate a systematic complexity-theoretic study of Colorful Components by presenting NP-hardness as well as fixed-parameter tractability results for different variants of Colorful Components. We also perform experiments with our algorithms and additionally develop an efficient and very accurate heuristic algorithm clearly outperforming a previous min-cut-based heuristic on multiple sequence alignment data.


Colorful Component Variable Cycle Satisfying Assignment Edge Deletion Network Alignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Avidor, A., Langberg, M.: The multi-multiway cut problem. Theoretical Computer Science 377(1-3), 35–42 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Fourier meets Möbius: fast subset convolution. In: Proc. 39th STOC, pp. 67–74. ACM (2007)Google Scholar
  3. 3.
    Böcker, S., Briesemeister, S., Bui, Q.B.A., Truß, A.: Going weighted: Parameterized algorthims for cluster editing. Theoretical Computer Science 410(52), 5467–5480 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bousquet, N., Daligault, J., Thomassé, S.: Multicut is FPT. In: Proc. 43rd STOC, pp. 459–468. ACM (2011)Google Scholar
  5. 5.
    Bruckner, S., Hüffner, F., Komusiewicz, C., Niedermeier, R.: Entity disambiguation by partitioning under heterogeneity constraints (manuscript, submitted) (February 2012),
  6. 6.
    Corel, E., Pitschi, F., Morgenstern, B.: A min-cut algorithm for the consistency problem in multiple sequence alignment. Bioinformatics 26(8), 1015–1021 (2010)CrossRefGoogle Scholar
  7. 7.
    Deniélou, Y.-P., Boyer, F., Viari, A., Sagot, M.-F.: Multiple Alignment of Biological Networks: A Flexible Approach. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 263–273. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Garg, N., Vazirani, V.V., Yannakakis, M.: Primal–dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18(1), 3–20 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. ACM SIGACT News 38(1), 31–45 (2007)CrossRefGoogle Scholar
  10. 10.
    Komusiewicz, C.: Parameterized Algorithmics for Network Analysis: Clustering & Querying. PhD thesis, Technische Universität Berlin, Berlin, Germany (2011)Google Scholar
  11. 11.
    Li, J., Yi, K., Zhang, Q.: Clustering with Diversity. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 188–200. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Lokshtanov, D., Marx, D., Saurabh, S.: Lower bounds based on the Exponential Time Hypothesis. Bulletin of the EATCS 105, 41–71 (2011)Google Scholar
  13. 13.
    Marx, D., Razgon, I.: Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: Proc. 43rd STOC, pp. 469–478. ACM (2011)Google Scholar
  14. 14.
    Park, D., Singh, R., Baym, M., Liao, C.-S., Berger, B.: IsoBase: a database of functionally related proteins across PPI networks. Nucleic Acids Research 39(Database), 295–300 (2011)CrossRefGoogle Scholar
  15. 15.
    Thompson, J.D., Koehl, P., Ripp, R., Poch, O.: BAliBASE 3.0: latest developments of the multiple sequence alignment benchmark. Proteins: Structure, Function, and Bioinformatics 61(1), 127–136 (2005)CrossRefGoogle Scholar
  16. 16.
    Weller, M., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: On making directed graphs transitive. Journal of Computer and System Sciences 78(2), 559–574 (2012)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sharon Bruckner
    • 1
  • Falk Hüffner
    • 2
  • Christian Komusiewicz
    • 2
  • Rolf Niedermeier
    • 2
  • Sven Thiel
    • 3
  • Johannes Uhlmann
    • 2
  1. 1.Institut für MathematikFreie Universität BerlinGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaGermany

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