Computing efficiently the lattice width in any dimension

We provide an algorithm for the exact computation of the lattice width of a set of points K in Z² in linear-time with respect to the size of K. This method consists in computing a particular surrounding polygon. From this polygon, we deduce a set of candidate vectors allowing the computation of the lattice width. Moreover, we describe how this new algorithm can be extended to an arbitrary dimension thanks to a greedy and practical approach to compute a surrounding polytope. Indeed, this last computation is very efficient in practice as it processes only a few linear time iterations whatever the size of the set of points. Hence, it avoids complex geometric processings.