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

The lattice A _n ^* is an important lattice because of its covering properties in low dimensions. Clarkson described an algorithm to compute the nearest lattice point in A _n ^* that requires O(n log n) arithmetic operations. In this correspondence, 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.