DeepAI
Log In Sign Up

Lifts for Voronoi cells of lattices

06/08/2021
by   Matthias Schymura, et al.
0

Many polytopes arising in polyhedral combinatorics are linear projections of higher-dimensional polytopes with significantly fewer facets. Such lifts may yield compressed representations of polytopes, which are typically used to construct small-size linear programs. Motivated by algorithmic implications for the closest vector problem, we study lifts of Voronoi cells of lattices. We construct an explicit d-dimensional lattice such that every lift of the respective Voronoi cell has 2^Ω(d / log d) facets. On the positive side, we show that Voronoi cells of d-dimensional root lattices and their dual lattices have lifts with O(d) and O(d log d) facets, respectively. We obtain similar results for spectrahedral lifts.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/16/2020

Logarithmic Voronoi cells

We study Voronoi cells in the statistical setting by considering preimag...
12/29/2021

Logarithmic Voronoi polytopes for discrete linear models

We study logarithmic Voronoi cells for linear statistical models and par...
03/03/2022

Logarithmic Voronoi Cells for Gaussian Models

We extend the theory of logarithmic Voronoi cells to Gaussian statistica...
04/21/2019

Constructive Polynomial Partitioning for Algebraic Curves in R^3 with Applications

In 2015, Guth proved that for any set of k-dimensional varieties in R^d ...
06/18/2019

A Note on Sequences of Lattices

We investigate the relation between the convergence of a sequence of lat...