A Polynomial Time Algorithm for Solving the Closest Vector Problem in Zonotopal Lattices

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