On the Computation of Hilbert Bases and Extreme Rays of Cones
Abstract
Description
In this paper we present a novel project-and-lift approach to compute the set of minimal generators of the semigroup $(Λ\cap\R^n_+,+)$ for lattices $Λ\subseteq\Z^n$. 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.