A paper by me and some Australian showed linear time algorithm for finding the closest lattice point in a family of lattices that includes A_n: https://www.itr.unisa.edu.au/itrusers/mckillrg/public_html/papers/ISITA_Anst... http://arxiv.org/abs/0903.0673 I don't know how the 2nd australian got on the paper as author. The squared-distance metric is arguably incorrect for this purpose for many applications, such as proportional representation voting. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)