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Algorithmica

, Volume 51, Issue 2, pp 129–159 | Cite as

Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs

  • Réka Albert
  • Bhaskar DasGupta
  • Riccardo Dondi
  • Eduardo Sontag
Article

Abstract

In this paper we consider the p-ary transitive reduction (TR p ) problem where p>0 is an integer; for p=2 this problem arises in inferring a sparsest possible (biological) signal transduction network consistent with a set of experimental observations with a goal to minimize false positive inferences even if risking false negatives. Special cases of TR p have been investigated before in different contexts; the best previous results are as follows:
  1. (1)

    The minimum equivalent digraph problem, that correspond to a special case of TR1 with no critical edges, is known to be MAX-SNP-hard, admits a polynomial time algorithm with an approximation ratio of 1.617+ε for any constant ε>0 (Chiu and Liu in Sci. Sin. 4:1396–1400, 1965) and can be solved in linear time for directed acyclic graphs (Aho et al. in SIAM J. Comput. 1(2):131–137, 1972).

     
  2. (2)

    A 2-approximation algorithm exists for TR1 (Frederickson and JàJà in SIAM J. Comput. 10(2):270–283, 1981; Khuller et al. in 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 937–938, 1999).

     
In this paper, our contributions are as follows:
  1. We observe that TR p , for any integer p>0, can be solved in linear time for directed acyclic graphs using the ideas in Aho et al. (SIAM J. Comput. 1(2):131–137, 1972).

     
  2. We provide a 1.78-approximation for TR1 that improves the 2-approximation mentioned in (2) above.

     
  3. We provide a 2+o(1)-approximation for TR p on general graphs for any fixed prime p>1.

     

Keywords

Transitive reduction of directed graphs Minimum equivalent digraph (Biological) signal transduction networks Approximation algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Réka Albert
    • 1
  • Bhaskar DasGupta
    • 2
  • Riccardo Dondi
    • 3
  • Eduardo Sontag
    • 4
  1. 1.Department of PhysicsPennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniversità degli Studi di BergamoBergamoItaly
  4. 4.Department of MathematicsRutgers UniversityNew BrunswickUSA

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