Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a possible stopping. We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give a motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research. (c) 2005 Elsevier B.V. All rights reserved.