Year: 2009
Type: article
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 \#\operatorname {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 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.
Source: Mathematics of Computation
Authors: Mathieu Dutour Sikirić, Achill Schürmann, Frank Vallentin
Institution: Centrum Wiskunde & Informatica
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W1971400259