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Some Results on More Flexible Versions of Graph Motif

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Abstract

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a vertex-colored graph. Due to the high rate of noise in the biological data, more flexible definitions of the problem have been outlined. We present in this paper two inapproximability results for two different optimization variants of Graph Motif: one where the size of the solution is maximized, the other when the number of substitutions of colors to obtain the motif from the solution is minimized. We also study a decision version of Graph Motif where the connectivity constraint is replaced by the well known notion of graph modularity. While the problem remains N P-complete, it allows algorithms in F P T for biologically relevant parameterizations.

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References

  1. Alm, E., Arkin, A.P.: Biological Networks. Curr. Opin. Struct. Biol. 13 (2), 193–202 (2003)

    Article  Google Scholar 

  2. Ambalath, A.M., Balasundaram, R., Rao, H.C., Koppula, V., Misra, N., Philip, G., Ramanujan, M.S.: On the Kernelization Complexity of Colorful Motifs. In: Raman, V., Saurabh, S. (eds.): Proceedings of the 5th International Symposium Parameterized and Exact Computation (IPEC), Lecture Notes in Computer Science, vol. 6478, pp. 14–25. Springer, Berlin (2010)

  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.): Proceedings of the 19th Annual Symposium Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science, vol. 5029, pp. 31–43. Springer, Berlin (2008)

  4. Björklund, A., Kaski, P., Kowalik, L.: Probably optimal graph motifs. In: Portier, N.,Wilke, T. (eds.): Proceedings of the 30th International Symposium on Theoretical Aspects of Computer Science (STACS), LIPIcs, vol. 20, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2012)

  5. Böcker, S., Rasche, F., Steijger, T.: Annotating Fragmentation Patterns. In: Salzberg, S., Warnow, T. (eds.) Proceedings of the 9th International Workshop Algorithms in Bioinformatics (WABI), Lecture Notes in Computer Science, Vol. 5724, pp 13–24. Springer, Berlin Heidelberg New York (2009)

  6. Bruckner, S., Hüffner, F., Karp, R.M., Shamir, R., Sharan, R.: Topology-Free Querying of Protein Interaction Networks. J. Comput. Biol. 17 (3), 237–252 (2010)

    Article  MathSciNet  Google Scholar 

  7. Chein, M., Habib, M., Maurer, M.C.: Partitive hypergraphs. Discret. Math. 37 (1), 35–50 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  8. Costanzo, M., Baryshnikova, A., Bellay, J., Kim, Y., Spear, E.D., Sevier, C.S., Ding, H., Koh, J.L.Y., Toufighi, K., Mostafavi, S., Prinz, J., St. Onge, R.P., VanderSluis, B., Makhnevych, T., Vizeacoumar, F.J., Alizadeh, S., Bahr, S., Brost, R.L., Chen, Y., Cokol, M., Deshpande, R., Li, Z., Lin, Z.Y., Liang, W., Marback, M., Paw, J., San Luis, B.J., Shuteriqi, E., Tong, A.H., van Dyk, N., Wallace, I.M., Whitney, J.A., Weirauch, M.T., Zhong, G., Zhu, H., Houry, W.A., Brudno, M., Ragibizadeh, S., Papp, B., Pál, C., Roth, F.P., Giaever, G., Nislow, C., Troyanskaya, O.G., Bussey, H., Bader, G.D., Gingras, A.C., Morris, Q.D., Kim, P.M., Kaiser, C.A., Myers, C.L., Andrews, B.J., Boone, C.: The genetic landscape of a cell. Sci. 327 (5964), 425–431 (2010)

    Article  Google Scholar 

  9. Cunningham, W.H.: Decomposition of directed graphs. SIAM J. Algebraic and Discret. Methods 3 (2), 214–228 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dahlhaus, E.: Parallel algorithms for hierarchical clustering and applications to split decomposition and parity graph recognition. J. Algorithm 36 (2), 205–240 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Del Mondo, G., Eveillard, D., Rusu, I.: Homogeneous decomposition of protein interaction networks: refining the description of intra-modular interactions. Bioinformatics 25 (7), 926–932 (2009)

    Article  Google Scholar 

  12. Dondi, R., Fertin, G., Vialette, S.: Complexity issues in vertex-colored graph pattern matching. J. Discr. Algo. 9(1), 82–99 (2011)

  13. Dondi, R., Fertin, G., Vialette, S.: Finding Approximate and Constrained Motifs in Graphs. In: Giancarlo, R., Manzini, G. (eds.) Proceedings of the 22nd Annual Symposium on Combinatorial Pattern Matching (CPM), Lecture Notes in Computer Science, Vol. 6661, pp 388–401. Springer, Berlin Heidelberg New York (2011)

  14. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer, Berlin (2013)

  15. Edwards, A.M., Kus, B., Jansen, R., Greenbaum, D., Greenblatt, J., Gerstein, M.: Bridging structural biology and genomics: assessing protein interaction data with known complexes. Trends Genet. 18 (10), 529–536 (2002)

    Article  Google Scholar 

  16. 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., Jurdzinski, T., Tarlecki, A. (eds.) Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, Vol. 4596, pp 340–351. Springer, Poland (2007)

  17. Gagneur, J., Krause, R., Bouwmeester, T., Casari, G.: Modular decomposition of protein-protein interaction networks. Genome Biol. 5 (8), R57 (2004)

    Article  Google Scholar 

  18. Guillemot, S., Sikora, F.: Finding and counting vertex-colored subtrees. Algorithmica 65 (4), 828–844 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  19. Habib, M., Montgolfier, F.d., Paul, C.: A Simple Linear-TimeModular Decomposition Algorithm for Graphs, Using Order Extension. In: Hagerup, T., Katajainen, J. (eds.): Proceedings of the 9th Scandinavian Workshop on Algorithm Theory (SWAT), Lecture Notes in Computer Science, vol. 3111, pp. 187–198. Springer, Berlin (2004)

  20. Khanna, S., Motwani, R., Sudan, M., Vazirani, U.: On syntactic versus computational views of approximability, In: Proceedings of the 35th Annual IEEE Annual Symposium on Foundations of Computer Science (FOCS), pp. 819–830 (1994)

  21. Koutis, I.: Constrained multilinear detection for faster functional motif discovery. Inf. Process. Lett. 112 (22), 889–892 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lacroix, V., Fernandes, C.G., Sagot, M.F.: Motif search in graphs: application to metabolic networks. IEEE/ACM Trans. Comput. Biol. Bioinforma. (TCBB) 3 (4), 360–368 (2006)

    Article  Google Scholar 

  23. Niedermeier, R.: Invitation to Fixed Parameter Algorithms. Lecture Series in Mathematics and Its Applications. Oxford University Press, London (2006)

    Book  Google Scholar 

  24. Ravasz, E., Somera, A.L., Mongru, D.A., Oltvai, Z.N., Barabasi, A.L.: Hierarchical Organization of Modularity in Metabolic Networks. Sci. 297 (5586), 1551–1555 (2002)

    Article  Google Scholar 

  25. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP, In: Proceedings of the 29th annual ACM Symposium on Theory of Computing (STOC), pp. 475–484. ACM (1997)

  26. Segal, E., Shapira, M., Regev, A., Pe’er, D., Botstein, D., Koller, D., Friedman, N.: Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data. Nat. Genet. 34 (2), 166–176 (2003)

    Article  Google Scholar 

  27. Sharan, R., Ideker, T.: Modeling cellular machinery through biological network comparison. Nat. Biotechnol. 24 (4), 427–433 (2006)

    Article  Google Scholar 

  28. Sikora, F.: Aspects algorithmiques de la comparaison d’éléments biologiques. Ph.D. thesis, Université Paris-Est. (in French) (2011)

  29. Zuckerman, D.: Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number. Theory Comput. 3 (1), 103–128 (2007)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Romeo Rizzi

  2. PSL Université Paris-Dauphine, LAMSADE, UMR CNRS 7243, Paris, France

    Florian Sikora

Authors
  1. Romeo Rizzi
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  2. Florian Sikora
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Correspondence to Florian Sikora.

Additional information

An extended abstract of this paper appeared in the proceedings of the 7th International Computer Science Symposium in Russia (CSR 2012), LNCS 7353, pp. 278-289.

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Rizzi, R., Sikora, F. Some Results on More Flexible Versions of Graph Motif. Theory Comput Syst 56, 612–629 (2015). https://doi.org/10.1007/s00224-014-9564-6

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  • DOI: https://doi.org/10.1007/s00224-014-9564-6

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