### Abstract

In this paper linear programming (LP)-based algorithms are presented to compute alternative structures (realizations) of biochemical reaction networks (CRNs) with mass action kinetics. The proposed algorithms have polynomial time complexity which enables us to handle large scale, biologically relevant problems. The main new contributions are the following: firstly, a new, effective LP-based method is presented that is guaranteed to compute the dense super-structure of a CRN, and secondly, it is shown that dynamically equivalent sparse structures can be computed efficiently and precisely by applying the theory of sparse nonnegative solutions of under-determined linear systems. It is shown through illustrative examples that the proposed methods outperform and thus can substitute the previously described MILP-based methods that are hard to tract computationally if the number of decision variables is high.

Original language | English |
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Pages (from-to) | 71-92 |

Number of pages | 22 |

Journal | Match |

Volume | 71 |

Issue number | 1 |

Publication status | Published - Apr 14 2014 |

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### ASJC Scopus subject areas

- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Match*,

*71*(1), 71-92.