Finding short vectors in a lattice of Voronoi's first kind

TL;DR

This paper demonstrates that for lattices of Voronoi's first kind, the shortest nonzero vector can be efficiently found using a polynomial-time algorithm based on graph minimum cut computations.

Contribution

It introduces a polynomial-time method for finding shortest vectors in Voronoi's first kind lattices using graph algorithms.

Findings

Shortest vectors in Voronoi's first kind lattices can be computed efficiently.

A polynomial-time algorithm based on minimum cut in a graph is effective.

The method improves upon previous approaches for these specific lattices.

Abstract

We show that for those lattices of Voronoi's first kind, a vector of shortest nonzero Euclidean length can computed in polynomial time by computing a minimum cut in a graph.