Finding and Counting Vertex-Colored Subtrees

  • Sylvain Guillemot
  • Florian Sikora
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)


The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. [17] in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors M. Using an algebraic framework recently introduced by Koutis et al. [15,16], we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, showing that the counting problem is FPT if M is a set, but becomes # W [1]-hard if M is a multiset with two colors.


Biological Network Connected Subgraph Counting Problem Arithmetic Circuit Algebraic Framework 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alm, E., Arkin, A.P.: Biological networks. Curr. Opin. Struct. Biol. 13(2), 193–202 (2003)CrossRefGoogle Scholar
  2. 2.
    Alon, N., Yuster, R., Zwick, U.: Color-coding. J. of ACM 42(4), 844–856 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Betzler, N., Fellows, M.R., Komusiewicz, C., Niedermeier, R.: Parameterized Algorithms and Hardness Results for Some Graph Motif Problems. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 31–43. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M.: Fourier meets möbius: fast subset convolution. In: STOC, pp. 67–74 (2007)Google Scholar
  5. 5.
    Blin, G., Sikora, F., Vialette, S.: GraMoFoNe: a Cytoscape plugin for querying motifs without topology in Protein-Protein Interactions networks. In: BICoB 2010, pp. 38–43 (2010)Google Scholar
  6. 6.
    Böcker, S., Rasche, F., Steijger, T.: Annotating Fragmentation Patterns. In: Salzberg, S.L., Warnow, T. (eds.) WABI 2009. LNCS (LNBI), vol. 5724, pp. 13–24. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Bruckner, S., Hüffner, F., Karp, R.M., Shamir, R., Sharan, R.: Topology-Free Querying of Protein Interaction Networks. In: Batzoglou, S. (ed.) RECOMB 2009. LNCS, vol. 5541, pp. 74–89. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Dondi, R., Fertin, G., Vialette, S.: Weak pattern matching in colored graphs: Minimizing the number of connected components. In: ICTCS, pp. 27–38 (2007)Google Scholar
  9. 9.
    Dondi, R., Fertin, G., Vialette, S.: Maximum Motif Problem in Vertex-Colored Graphs. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 221–235. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Fellows, M.R., Fertin, G., Hermelin, D., Vialette, S.: Sharp Tractability Borderlines for Finding Connected Motifs in Vertex-Colored Graphs. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 340–351. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Flum, J., Grohe, M.: The Parameterized Complexity of Counting Problems. SIAM Journal on Computing 33(4), 892–922 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)Google Scholar
  13. 13.
    Hüffner, F., Wernicke, S., Zichner, T.: Algorithm Engineering For Color-Coding To Facilitate Signaling Pathway Detection. In: APBC 2007, pp. 277–286 (2007)Google Scholar
  14. 14.
    Karp, R.M.: Dynamic-programming meets the principle of inclusion and exclusion. Oper. Res. Lett. 1, 49–51 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Koutis, I.: Faster Algebraic Algorithms for Path and Packing Problems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 575–586. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Koutis, I., Williams, R.: Limits and Applications of Group Algebras for Parameterized Problems. In: Albers, S., et al. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 653–664. Springer, Heidelberg (2009)Google Scholar
  17. 17.
    Lacroix, V., Fernandes, C.G., Sagot, M.-F.: Motif Search in Graphs: Application to Metabolic Networks. Trans. Comput. Biol. Bioinform. 3(4), 360–368 (2006)CrossRefGoogle Scholar
  18. 18.
    Nederlof, J.: Fast Polynomial-Space Algorithms Using Möbius Inversion: Improving on Steiner Tree and Related Problems. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 713–725. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Schbath, S., Lacroix, V., Sagot, M.-F.: Assessing the exceptionality of coloured motifs in networks. In: EURASIP JBSB, pp. 1–9 (2009)Google Scholar
  20. 20.
    Sharan, R., Ideker, T.: Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, 427–433 (2006)CrossRefGoogle Scholar
  21. 21.
    Williams, R.: Finding paths of length k in O *(2k) time. IPL 109(6), 315–318 (2009)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sylvain Guillemot
    • 1
  • Florian Sikora
    • 2
  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller Universität JenaJenaGermany
  2. 2.Université Paris-Est, LIGM - UMR CNRSFrance

Personalised recommendations