The Exact Lattice Width of Planar Sets and Minimal Arithmetical Thickness

We provide in this paper an algorithm for the exact computation of the lattice width of an integral polygon K with n vertices in O(n log s) arithmetic operations where s is a bound on all integers defining vertices and edges. We also provide an incremental version of the algorithm whose update complexity is shown to be O(log n + log s). We apply this algorithm to construct the arithmetical line with minimal thickness, which contains a given set of integer points.

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