  We show that for those lattices of Voronoi's first kind with known obtuse
superbasis, a closest lattice point can be computed in $O(n^4)$ 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 $O(n^3)$ operations using an algorithm to
compute a minimum cut in an undirected flow network.
