Exploiting Bounded Signal Flow for Graph Orientation Based on Cause–Effect Pairs

  • Britta Dorn
  • Falk Hüffner
  • Dominikus Krüger
  • Rolf Niedermeier
  • Johannes Uhlmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6595)

Abstract

We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows” defined by the pairs can be routed respecting edge directions. This problem has applications in communication networks and in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. For many relevant cases, the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.

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References

  1. 1.
    Alm, E., Arkin, A.P.: Biological networks. Current Opinion in Structural Biology 13(2), 193–202 (2003)CrossRefGoogle Scholar
  2. 2.
    Arnborg, S., Proskurowski, A.: Characterization and recognition of partial 3-trees. SIAM Journal on Algebraic and Discrete Methods 7(2), 305–314 (1986)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bruckner, S., Hüffner, F., Karp, R.M., Shamir, R., Sharan, R.: Topology-free querying of protein interaction networks. Journal of Computational Biology 17(3), 237–252 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  5. 5.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)MATHGoogle Scholar
  6. 6.
    Gamzu, I., Segev, D., Sharan, R.: Improved orientations of physical networks. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 215–225. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Guo, J., Hüffner, F., Niedermeier, R.: A structural view on parameterizing problems: distance from triviality. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 162–173. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Hakimi, S.L., Schmeichel, E.F., Young, N.E.: Orienting graphs to optimize reachability. Information Processing Letters 63(5), 229–235 (1997)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Medvedovsky, A., Bafna, V., Zwick, U., Sharan, R.: An algorithm for orienting graphs based on cause-effect pairs and its applications to orienting protein networks. In: Crandall, K.A., Lagergren, J. (eds.) WABI 2008. LNCS (LNBI), vol. 5251, pp. 222–232. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and Its Applications, vol. 31. Oxford University Press, Oxford (2006)CrossRefMATHGoogle Scholar
  11. 11.
    Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proc. 27th STACS. Leibniz International Proceedings in Informatics, vol. 5, pp. 17–32. Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)Google Scholar
  12. 12.
    Salwinski, L., Miller, C.S., Smith, A.J., Pettit, F.K., Bowie, J.U., Eisenberg, D.: The database of interacting proteins: 2004 update. Nucleic Acids Research 32(Database issue), D449–D451 (2004)Google Scholar
  13. 13.
    Sharan, R., Ideker, T.: Modeling cellular machinery through biological network comparison. Nature Biotechnology 24, 427–433 (2006)CrossRefGoogle Scholar
  14. 14.
    Silverbush, D., Elberfeld, M., Sharan, R.: Optimally orienting physical networks. In: Proc. 15th RECOMB. LNCS. Springer, Heidelberg (to appear, 2011)Google Scholar
  15. 15.
    Yeang, C.H., Ideker, T., Jaakkola, T.: Physical network models. Journal of Computational Biology 11(2-3), 243–262 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Britta Dorn
    • 1
  • Falk Hüffner
    • 2
  • Dominikus Krüger
    • 3
  • Rolf Niedermeier
    • 4
  • Johannes Uhlmann
    • 4
  1. 1.Fakultät für Mathematik und WirtschaftswissenschaftenUniversität UlmUlmGermany
  2. 2.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Institut für Theoretische InformatikUniversität UlmUlmGermany
  4. 4.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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