Year: 2021
Type: article
Abstract: In this note we give a polynomial time algorithm for solving the closest vector problem in the class of zonotopal lattices. The Voronoi cell of a zonotopal lattice is a zonotope, i.e., a projection of a regular cube. Examples of zonotopal lattices include lattices of Voronoi's first kind and tensor products of root lattices of type $\mathsf{A}$. The combinatorial structure of zonotopal lattices can be described by regular matroids/totally unimodular matrices. We observe that a linear algebra version of the minimum mean cycle canceling method can be applied for efficiently solving the closest vector problem in a zonotopal lattice if the lattice is given as the integral kernel of a totally unimodular matrix.
DOI: 10.1137/20m1382258
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3016695087