Parameterized Complexity of Finding Elementary Modes in Metabolic Networks

The concept of elementary (flux) modes provides a rigorous description of pathways in metabolic networks. Finding the elementary modes with minimum number of reactions (shortest elementary modes) is an interesting problem and has potential uses in various applications. However, this problem is NP-hard. This work is an initial step to analyze this problem from a parameterized computation view. With the number of reactions in elementary modes as natural parameter, we prove that finding the shortest elementary modes in metabolic networks is W-hard.