2022
DOI: 10.1007/s00493-020-4633-8
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Computing the Covering Radius of a Polytope with an Application to Lonely Runners

Abstract: We study the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed for the lattice translates of the correspondingly dilated polytope to cover the whole space. As our main result, we describe a new algorithm for this problem, which is simpler, more efficient and easier to implement than the only prior algorithm of Kannan (1992).Motivated by a variant of the famous Lonely Runner Conjecture, we use its geometric in… Show more

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