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

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) 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) operations using an algorithm to compute a minimum cut in an undirected flow network.