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arXiv · 1401.0040

Voronoi Polytopes for Polyhedral Norms on Lattices

Michel Deza·Mathieu Dutour Sikirić
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Abstract

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.

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Michel Deza, Mathieu Dutour Sikirić. 2013-12-30. Voronoi Polytopes for Polyhedral Norms on Lattices. https://arxiv.org/abs/1401.0040

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