Exact Algorithms for Finding a Minimum Reaction Cut under a Boolean Model of Metabolic Networks

A reaction cut is a set of chemical reactions whose deletion blocks the operation of given reactions or the production of given chemical compounds. In this paper, we study two problems ReactionCut and MD-ReactionCut for calculating the minimum reaction cut of a metabolic network under a Boolean model. These problems are based on the flux balance model and the minimal damage model respectively. We show that ReactionCut and MD-ReactionCut are NP-hard even if the maximum outdegree of reaction nodes (Kout) is one. We also present O(1.822n), O(1.959n) and o(2n) time algorithms for MD-ReactionCut with Kout = 2, 3, k respectively where n is the number of reaction nodes and k is a constant. The same algorithms also work for ReactionCut if there is no directed cycle. Furthermore, we present a 2O((log n)√n) time algorithm, which is faster than O((1+e)n) for any positive constant e, for the planar case of MD-ReactionCut under a reasonable constraint utilizing Lipton and Tarjan's separator algorithm.

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