On the Computation of Hilbert Bases and Extreme Rays of Cones

Details On the Computation of Hilbert Bases and Extreme Rays of Cones On the Computation of Hilbert Bases and Extreme Rays of Cones

2002-03-12

arxiv.org/abs/math/0203105v1

Mathematics

Combinatorics

Scientific paper

In this paper we present a novel project-and-lift approach to compute the set of minimal generators of the semigroup $(\Lambda\cap\R^n_+,+)$ for lattices $\Lambda\subseteq\Z^n$. This problem class includes the computation of Hilbert bases of cones $\{z:Az=0,z\in\R^n_+\}$ for integer matrices $A$. A similar approach can be used to compute only the extreme rays of such cones. Finally, some combinatorial applications and computational experience are presented.

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