Advertisement

Sharp Tractability Borderlines for Finding Connected Motifs in Vertex-Colored Graphs

  • Michael R. Fellows
  • Guillaume Fertin
  • Danny Hermelin
  • Stéphane Vialette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

We study the problem of finding occurrences of motifs in vertex-colored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices whose multiset of colors equals the motif. This problem has applications in metabolic network analysis, an important area in bioinformatics. We give two positive results and three negative results that together draw sharp borderlines between tractable and intractable instances of the problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abrahamson, K.R., Fellows, M.R.: Finite automata, bounded treewidth, and well-quasiordering. In: Robertson, N., Seymoued, P. (eds.), Graph Structure Theory, pp. 539–564 (1993)Google Scholar
  2. 2.
    Alon, N., Yuster, R., Zwick, U.: Color coding. Journal of the ACM 42(4), 844–856 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arnborg, S.: Efficient algorithms for combinatorial problems on graphs with bounded decomposability. A survey. BIT Numerical Mathematics 25(1), 2–23 (1985)MATHMathSciNetGoogle Scholar
  4. 4.
    Arnborg, S., Proskurowski, A.: Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics 23, 11–24 (1989)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybernetica 11, 1–23 (1993)MATHMathSciNetGoogle Scholar
  6. 6.
    Bodlaender, H.L., Fluiter, L.E.: Intervalizing k-colored graphs. In: Fülöp, Z., Gecseg, F. (eds.) Automata, Languages and Programming. LNCS, vol. 944, pp. 87–98. Springer, Heidelberg (1995)Google Scholar
  7. 7.
    Bodlaender, H.L., Fellows, M.R., Langston, M.A., Ragan, M.A., Rosamond, F.A., Weyer, M.: Kernelization for convex recoloring. In: Proceedings of the 2nd workshop on Algorithms and Complexity in Durham (ACiD), pp. 23–35 (2006)Google Scholar
  8. 8.
    Bodlaender, H.L., Fellows, M.R., Warnow, T.: Two strikes against perfect phylogeny. In: Kuich, W. (ed.) Automata, Languages and Programming. LNCS, vol. 623, pp. 273–283. Springer, Heidelberg (1992)Google Scholar
  9. 9.
    Chor, B., Fellows, M.R., Ragan, M.A., Rosamond, F.A., Snir, S.: Connected coloring completion for general graphs: Algorithms and complexity – Manuscript (2007)Google Scholar
  10. 10.
    Corneil, D.G., Keil, J.M.: A dynamic programming approach to the dominating set problem on k-trees. SIAM Journal on Algebraic and Discrete Methods 8(4), 535–543 (1987)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Deville, Y., Gilbert, D., Helden, J.V., Wodak, S.J.: An overview of data models for the analysis of biochemical pathways. Briefings in Bioinformatics 4(3), 246–259 (2003)CrossRefGoogle Scholar
  12. 12.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  13. 13.
    Fellows, M.R., Hallett, M.T., Wareham, H.T.: DNA physical mapping: Three ways difficult. In: Lengauer, T. (ed.) ESA 1993. LNCS, vol. 726, pp. 157–168. Springer, Heidelberg (1993)Google Scholar
  14. 14.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)MATHGoogle Scholar
  15. 15.
    Golumbic, M., Kaplan, H., Shamir, R.: On the complexity of DNA physical mapping. Advances in Applied Mathematics 15, 251–261 (1994)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Ideker, T., Karp, R.M., Scott, J., Sharan, R.: Efficient algorithms for detecting signaling pathways in protein interaction networks. Journal of Computational Biology 13(2), 133–144 (2006)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Kelley, B.P., Sharan, R., Karp, R.M., Sittler, T., Root, D.E., Stockwell, B.R., Ideker, T.: Conserved pathways within bacteria and yeast as revealed by global protein network alignment. Proceedings of the National Academy of Sciences of the United States of America 100(20), 11394–11399 (2003)CrossRefGoogle Scholar
  18. 18.
    Lacroix, V., Fernandes, C.G., Sagot, M.-F.: Motif search in graphs: Application to metabolic networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(4), 360–368 (2006)CrossRefGoogle Scholar
  19. 19.
    McMorris, F.R., Warnow, T.J., Wimer, T.: Triangulating vertex-colored graphs. SIAM Journal on Discrete Mathematics 7(2), 296–306 (1994)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Moran, S., Snir, S.: Convex recolorings of strings and trees: Definitions, hardness results and algorithms. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 218–232. Springer, Heidelberg (2005)Google Scholar
  21. 21.
    Naor, J., Naor, M.: Small-bias probability spaces: Efficient constructions and applications. In: STOC. Proceedings of the 25th annual ACM Symposium on Theory Of Computing, pp. 213–223. ACM Press, New York (1990)Google Scholar
  22. 22.
    Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. SIAM Journal of Algorithms 7, 309–322 (1986)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Michael R. Fellows
    • 1
    • 2
  • Guillaume Fertin
    • 3
  • Danny Hermelin
    • 4
  • Stéphane Vialette
    • 5
  1. 1.The University of Newcastle, Callaghan NSW 2308Australia
  2. 2.Institute of Advanced Study, Durham University, Durham DH1 3RLUnited Kingdom
  3. 3.Laboratoire d’Informatique de Nantes-Atlantique (LINA), FRE CNRS 2729, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes Cedex 3France
  4. 4.Department of Computer Science, University of Haifa, Mount Carmel, Haifa 31905Israel
  5. 5.Laboratoire de Recherche en Informatique (LRI), UMR CNRS 8623, Faculté des Sciences d’Orsay - Université Paris-Sud, 91405 OrsayFrance

Personalised recommendations