Algorithmic and complexity results for decompositions of biological networks into monotone subsystems

Bhaskar DasGupta, German Andres Enciso, Eduardo Sontag, Yi Zhang

Research output: Contribution to journalArticle

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A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson [Goemans, M., Williamson, D., 1995. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42 (6), 1115-1145]. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.

Original languageEnglish (US)
Pages (from-to)161-178
Number of pages18
Issue number1
StatePublished - Jul 1 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics


  • Approximation algorithms
  • Biological networks
  • Monotone dynamical systems
  • Semidefinite programming
  • Sign-consistent subgraphs

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