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arXiv · 1405.7014

Finding a closest point in a lattice of Voronoi's first kind

Robby G. McKilliam·Alex Grant·I. Vaughan L. Clarkson
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Abstract

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.

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Robby G. McKilliam, Alex Grant, I. Vaughan L. Clarkson. 2014-05-27. Finding a closest point in a lattice of Voronoi's first kind. https://arxiv.org/abs/1405.7014

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