Computing all possible graph structures describing linearly conjugate realizations of kinetic systems

TL;DR

This paper presents an algorithm to enumerate all structurally different linearly conjugate realizations of a kinetic polynomial system, using linear programming to efficiently explore the exponentially large space of possible graph structures.

Contribution

The paper introduces a novel algorithm that systematically finds all distinct reaction graph structures for a given kinetic system, with a focus on computational efficiency and correctness.

Findings

Algorithm successfully enumerates all realizations in organized manner

Polynomial time between consecutive realizations

Illustrative examples demonstrate practical operation

Abstract

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.