Computing the Covering Radius of a Polytope with an Application to Lonely Runners

We study the computational problem of determining covering radius a rational polytope. This parameter is defined as minimal dilation factor that needed for lattice translates correspondingly dilated polytope to cover whole space. As our main result, we describe new algorithm this problem, which simpler, more efficient and easier implement than only prior Kannan (1992). Motivated by variant famous Lonely Runner Conjecture, use its geometric interpretation in terms radii zonotopes, apply prove first open case three runners with individual starting points.