Voronoi polytopes for polyhedral norms on lattices
Copyright policy )Voronoi polytopes for polyhedral norms on lattices
A polyhedral norm is a norm N on R^n for which the set N(x)\leq 1 is a polytope. This covers the case of the L^1 and L^{\infty} norms. We consider here effective algorithms for determining the Voronoi polytope for such norms with a point set being a lattice. The algorithms, that we propose, use the symmetries effectively in order to compute a decomposition of the space into convex polytopes named {\em $VN$-spaces}. The Voronoi polytopes and other geometrical information are easily obtained from it.
18 pages, 3 figures
- École Normale Supérieure France
Voronoi polytope; affine hyperplane arrangements; enumeration, Voronoi polytope, Metric Geometry (math.MG), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), affine hyperplane arrangements, enumeration, Voronoi polytopes, Mathematics - Metric Geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
Voronoi polytope; affine hyperplane arrangements; enumeration, Voronoi polytope, Metric Geometry (math.MG), Arrangements of points, flats, hyperplanes (aspects of discrete geometry), affine hyperplane arrangements, enumeration, Voronoi polytopes, Mathematics - Metric Geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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