Complexity and algorithms for computing Voronoi cells of lattices
Metric Geometry
2009-05-04 v4 Computational Geometry
Information Theory
math.IT
Number Theory
Abstract
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm for this problem which is especially suited for low dimensional (say dimensions at most 12) and for highly-symmetric lattices. We use our implementation, which drastically outperforms those of current computer algebra systems, to find the vertices of Voronoi cells and quantizer constants of some prominent lattices.
Cite
@article{arxiv.0804.0036,
title = {Complexity and algorithms for computing Voronoi cells of lattices},
author = {Mathieu Dutour Sikiric and Achill Schuermann and Frank Vallentin},
journal= {arXiv preprint arXiv:0804.0036},
year = {2009}
}
Comments
20 pages, 2 figures, 5 tables