Adjacency method for extreme Delaunay polytopes

@misc{citeulike:2967827, abstract = {The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme rays are called {\em extreme}. We use this polyhedral cone and the {\em closest vector problem} to present a new technique that allow to find, from a given extreme Delaunay polytope, some new ones. Then, we show some examples of applications of this technique in low-dimensions.}, author = {Dutour, Mathieu }, citeulike-article-id = {2967827}, eprint = {math/0401004}, keywords = {convex, delaunay, metric}, month = {Jan}, posted-at = {2008-07-06 21:06:54}, priority = {2}, title = {Adjacency method for extreme Delaunay polytopes}, url = {http://arxiv.org/abs/math/0401004}, year = {2004} }

TY - ELEC ID - citeulike:2967827 L3 - citeulike-article-id:2967827 TI - Adjacency method for extreme Delaunay polytopes N2 - The {\em hypermetric cone} is defined as the cone of semimetrics satisfying the {\em hypermetric inequalities}. Every {\em Delaunay polytope} corresponds to a ray of this polyhedral cone. The Delaunay polytopes, which correspond to extreme rays are called {\em extreme}. We use this polyhedral cone and the {\em closest vector problem} to present a new technique that allow to find, from a given extreme Delaunay polytope, some new ones. Then, we show some examples of applications of this technique in low-dimensions. KW - convex KW - delaunay KW - metric AU - Dutour, Mathieu PY - 2004/Jan/02/ UR - http://arxiv.org/abs/math/0401004 ER -