An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$

Robby G. McKilliam; I. Vaughan L. Clarkson; Barry G. Quinn

doi:10.1109/tit.2008.928280

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arXiv · 0801.1364

An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$

Robby G. McKilliam·I. Vaughan L. Clarkson·Barry G. Quinn

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Abstract

The lattice $A_n^*$ is an important lattice because of its covering properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an algorithm to compute the nearest lattice point in $A_n^*$ that requires $O(n\log{n})$ arithmetic operations. In this paper, we describe a new algorithm. While the complexity is still $O(n\log{n})$, it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.

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Robby G. McKilliam, I. Vaughan L. Clarkson, Barry G. Quinn. 2008-09-30. An Algorithm to Compute the Nearest Point in the Lattice $A_{n}^*$. https://doi.org/10.1109/tit.2008.928280

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