  In this note we give a polynomial time algorithm for solving the closest
vector problem in the class of zonotopal lattices. The Voronoi cell of a
zonotopal lattice is a zonotope, i.e. a projection of a regular cube. Examples
of zonotopal lattices include lattices of Voronoi's first kind and tensor
products of root lattices of type A. The combinatorial structure of zonotopal
lattices can be described by regular matroids/totally unimodular matrices. We
observe that a linear algebra version of the minimum mean cycle canceling
method can be applied for efficiently solving the closest vector problem in a
zonotopal lattice if the lattice is given as the integral kernel of a totally
unimodular matrix.
