Principles of automated theorem proving
Principles of automated theorem proving
Near-optimal nonapproximability results for some NPO PB-complete problems
Information Processing Letters
The Complexity of Illuminating Polygons by alpha-flood-lights
Proceedings of the 8th Canadian Conference on Computational Geometry
Metabolic Network Expansion with Answer Set Programming
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem
Journal of Discrete Algorithms
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For a given metabolic network, we address the problem of determining the minimum cardinality set of substrate compounds necessary for synthesizing a set of target metabolites, called the inverse scope problem. We define three variants of the inverse scope problem whose solutions may indicate minimal nutritional requirements that must be met to ensure sustenance of an organism, with or without some side products. Here, we show that the inverse scope problems are NP-hard on general graphs and directed acyclic graphs (DAGs). Moreover, we show that the general inverse scope problem cannot be approximated within n1/2 驴 驴for any constant 驴 0 unless P = NP. Our results have direct implications for identifying the biosynthetic capabilities of a given organism and for designing biochemical experiments.