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

A polynomial time algorithm for solving the closest vector problem in zonotopal lattices