Computing all possible graph structures describing linearly conjugate realizations of kinetic systems
For researchers in chemical reaction network theory, this provides a systematic method to explore all possible reaction graph structures for a given kinetic system.
The paper presents an algorithm to enumerate all structurally different linearly conjugate realizations of a kinetic polynomial system, using linear programming for constrained dense realizations. The algorithm ensures polynomial time between consecutive outputs, demonstrated on two examples.
In this paper an algorithm is given to determine all possible structurally different linearly conjugate realizations of a given kinetic polynomial system. The solution is based on the iterative search for constrained dense realizations using linear programming. Since there might exist exponentially many different reaction graph structures, we cannot expect to have a polynomial-time algorithm, but we can organize the computation in such a way that polynomial time is elapsed between displaying any two consecutive realizations. The correctness of the algorithm is proved, and possibilities of a parallel implementation are discussed. The operation of the method is shown on two illustrative examples.