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Kissing polytopes

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arxiv 2305.18597 v2 pith:65DXIIJ5 submitted 2023-05-29 math.MG math.COmath.OC

Kissing polytopes

Antoine Deza , Shmuel Onn , Sebastian Pokutta , Lionel Pournin This is my paper
classification math.MG math.COmath.OC
keywords polytopesboundsdisjointdistancequestionalgorithmsappearsbinary
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We investigate the following question: how close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching lower and upper bounds on this distance and discuss its exact computation. We also give similar bounds in the case of disjoint rational polytopes whose binary encoding length is prescribed.

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