Voronoi Cells of Lattices with Respect to Arbitrary Norms

@article{Blmer2018VoronoiCO,
  title={Voronoi Cells of Lattices with Respect to Arbitrary Norms},
  author={Johannes Bl{\"o}mer and Kathl{\'e}n Kohn},
  journal={ArXiv},
  year={2018},
  volume={abs/1512.00720}
}
We study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show for strictly convex and smooth norms that the geometry of Voronoi cells of lattices in any dimension is similar to the Euclidean case, i.e., the Voronoi cells are defined by the so-called Voronoi-relevant vectors and the facets of a Voronoi cell are in one-to-one correspondence with these vectors. On the negative side, we show that Voronoi cells are combinatorially… Expand
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