On the parameterized complexity of the problem of inferring protein–protein interaction directions based on cause–effect pairs

  • Mehdy RoayaeiEmail author
Original Article


We consider the following problem: given an undirected (mixed) network and a set of ordered source–target pairs, or cause–effect pairs, direct all edges so as to maximize the number of pairs that admit a directed source–target path. This is called the maximum graph orientation problem, and has applications in understanding interactions in protein–protein interaction networks. Since this problem is NP-hard, we take the parameterized complexity viewpoint and study the parameterized (in)tractability of the problem with respect to various parameters on both undirected and mixed networks. In the undirected case, we determine the parameterized complexity of the problem (for non-fixed and fixed paths) with respect to the number of satisfied pairs. Also, we present an exact algorithm which outperforms the previous algorithms on trees with bounded number of leaves. In the mixed case, we present polynomial-time algorithms for the problem on paths and cycles, and an FPT algorithm with respect to the combined parameter number of arcs and number of pairs on general graphs.


Protein–protein interaction network Cause–effect pairs Parameterized complexity Fixed-parameter tractable W[1]-hardness 


  1. Arkin EM, Hassin R (2002) A note on orientations of mixed graphs. Discrete Appl Math 116(3):271–278MathSciNetCrossRefGoogle Scholar
  2. Böcker S, Damaschke P (2012) A note on the parameterized complexity of unordered maximum tree orientation. Discrete Appl Math 160(10–11):1634–1638MathSciNetCrossRefGoogle Scholar
  3. Chen JE (2005) Parameterized computation and complexity: a new approach dealing with NP-hardness. J Comput Sci Technol 20(1):18–37MathSciNetCrossRefGoogle Scholar
  4. Chen J, Feng QL (2014) On unknown small subsets and implicit measures: new techniques for parameterized algorithms. J Comput Sci Technol 29(5):870–878MathSciNetCrossRefGoogle Scholar
  5. Dorn B, Hüffner F, Krüger D, Niedermeier R, Uhlmann J (2011) Exploiting bounded signal flow for graph orientation based on cause–effect pairs. Algorithm Mol Biol 6(1):21CrossRefGoogle Scholar
  6. Downey RG, Fellows MR (2013) Fundamentals of parameterized complexity, vol 4. Springer, LondonCrossRefGoogle Scholar
  7. Elberfeld M, Segev D, Davidson CR, Silverbush D, Sharan R (2013) Approximation algorithms for orienting mixed graphs. Theor Comput Sci 483:96–103MathSciNetCrossRefGoogle Scholar
  8. Erdös P, Szekeres G (1935) A combinatorial problem in geometry. Compos Math 2:463–470MathSciNetzbMATHGoogle Scholar
  9. Fields S (2005) High-throughput two-hybrid analysis. FEBS J 272(21):5391–5399CrossRefGoogle Scholar
  10. Gamzu I, Medina M (2016) Improved approximation for orienting mixed graphs. Algorithmica 74(1):49–64MathSciNetCrossRefGoogle Scholar
  11. Gamzu I, Segev D, Sharan R (2010) Improved orientations of physical networks. In: Moulton V, Singh M (eds) Algorithms in bioinformatics. WABI 2010. Lecture notes in computer science, vol 6293. Springer, Berlin, pp 215–225Google Scholar
  12. Gavin AC, Bösche M, Krause R, Grandi P, Marzioch M, Bauer A, Remor M (2002) Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415(6868):141CrossRefGoogle Scholar
  13. Medvedovsky A, Bafna V, Zwick U, Sharan R (2008) An algorithm for orienting graphs based on cause-effect pairs and its applications to orienting protein networks. In: Crandall KA, Lagergren J (eds) Algorithms in bioinformatics. WABI 2008. Lecture notes in computer science, vol 5251. Springer, Berlin, pp 222–232Google Scholar
  14. Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, UKCrossRefGoogle Scholar
  15. Silverbush D, Elberfeld M, Sharan R (2011) Optimally orienting physical networks. J Comput Biol 18(11):1437–1448MathSciNetCrossRefGoogle Scholar
  16. Yeang CH, Ideker T, Jaakkola T (2004) Physical network models. J Comput Biol 11(2–3):243–262CrossRefGoogle Scholar
  17. Zhao X, Ding D (2003) Fixed-parameter tractability of disjunction-free default reasoning. J Comput Sci Technol 18(1):118MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Tarbiat Modares UniversityTehranIran

Personalised recommendations