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

The lattice <i>A</i> <sub>n</sub> <sup>*</sup> is an important lattice because of its covering properties in low dimensions. Clarkson described an algorithm to compute the nearest lattice point in <i>A</i> <sub>n</sub> <sup>*</sup> that requires <i>O</i>(<i>n</i> log <i>n</i>) arithmetic operations. In this correspondence, we describe a new algorithm. While the complexity is still <i>O</i>(<i>n</i> log <i>n</i>), it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.

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