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Computer Science, Symbolic Computation, cs.SC,Mathematics, Commutative Algebra, math.AC
Abstract:
We study binomiality of the steady state ideals of chemical reaction
networks. Considering rate constants as indeterminates, the concept of
unconditional binomiality has been introduced and an algorithm based on linear
algebra has been proposed in a recent work for reversible chemical reaction
networks, which has a polynomial time complexity upper bound on the number of
species and reactions. In this article, using a modified version of
species--reaction graphs, we present an algorithm based on graph theory which
performs by adding and deleting edges and changing the labels of the edges in
order to test unconditional binomiality. We have implemented our graph
theoretical algorithm as well as the linear algebra one in Maple and made
experiments on biochemical models. Our experiments show that the performance of
the graph theoretical approach is similar to or better than the linear algebra
approach, while it is drastically faster than Groebner basis and quantifier
elimination methods.
