An Explicit Upper Bound for the Approximation Ratio of the Maximum Gene Regulatory Network Problem

  • Sergio Pozzi
  • Gianluca Della Vedova
  • Giancarlo Mauri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3082)

Abstract

One of the combinatorial models for the biological problem of inferring gene regulation networks is the Maximum Gene Regulatory Network Problem, shortly MGRN, proposed in [2]. The problem is NP-hard [2], consequently the attention has shifted towards approximation algorithms, leading to a polynomial-time 1/2-approximation algorithm [2], while no upper bound on the possible approximation ratio was previously known.

In this paper we make a first step towards closing the gap between the best known and the best possible approximation factors, by showing that no polynomial-time approximation algorithm can have a factor better than 1 – (1/8) / (1+e2) unless RP=NP.

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References

  1. 1.
    Akutsu, T., Kuhara, S., Maruyama, O., Miyano, S.: Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions. In: Proc. 9th Symp. on Discrete Algorithms (SODA), pp. 695–702 (1998)Google Scholar
  2. 2.
    Chen, T., Filkov, V., Skiena, S.S.: Identifying gene regulatory networks from experimental data. Parallel Computing 27, 317–330 (1999)MATHGoogle Scholar
  3. 3.
    Consortium, I.H.G.S.: Initial sequencing and analysis of the human genome. Nature 409, 860–921 (2001)CrossRefGoogle Scholar
  4. 4.
    Håstad, J.: Some optimal inapproximability results. Journal of the ACM 48, 798–859 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Liang, S., Fuhrman, S., Somogyi, R.: Reveal, a general reverse engineering algorithm for inference of genetic network architectures. In: Proc. 5th Pacific Symposium on Biocomputing (PSB), pp. 18–29 (1998)Google Scholar
  6. 6.
    Soulé, C.: Graphic requirements for multistationarity. ComPlexUs 1, 123–133 (2003)CrossRefGoogle Scholar
  7. 7.
    Thomas, R., Gathoye, A., Lambert, L.A.: A complex control circuit. regulation of immunity in temperate bacteriophage. European Journal of Biochemistry 71, 211–227 (1976)CrossRefGoogle Scholar
  8. 8.
    Trevisan, L.: Non-approximability results for optimization problems on bounded degree instances. In: Proc. 33rd Symp. Theory of Computing (STOC), pp. 453–461 (2001)Google Scholar
  9. 9.
    Venter, J.C., Adams, M.D., Myers, E.W., et al.: The sequence of the human genome. Science 291, 1304–1351 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sergio Pozzi
    • 1
  • Gianluca Della Vedova
    • 2
  • Giancarlo Mauri
    • 1
  1. 1.DISCo, Univ. Milano-BicoccaItaly
  2. 2.Dip. StatisticaUniv. Milano-BicoccaItaly

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