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Information Processing Letters
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The vertex set of a 0/1-polytope is strongly P-enumerable
Computational Geometry: Theory and Applications
Journal of the ACM (JACM)
An Algorithm for Convex Polytopes
Journal of the ACM (JACM)
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SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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A note on systems with max--min and max-product constraints
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VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
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Complexity of Approximating the Vertex Centroid of a Polyhedron
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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Maximum delay computation for interdomain path selection
International Journal of Network Management
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We show that generating all negative cycles of a weighted graph is a hard enumeration problem, in both the directed and undirected cases. More precisely, given a family of negative (directed) cycles, it is an NP-complete problem to decide whether this family can be extended or there are no other negative (directed) cycles in the graph, implying that (directed) negative cycles cannot be generated in polynomial output time, unless P=NP. As a corollary, we solve in the negative two well-known generating problems from linear programming: (i) Given an infeasible system of linear inequalities, generating all minimal infeasible subsystems is hard. Yet, for generating maximal feasible subsystems the complexity remains open. (ii) Given a feasible system of linear inequalities, generating all vertices of the corresponding polyhedron is hard. Yet, in the case of bounded polyhedra the complexity remains open