  We are concerned with 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 interpretation in terms of covering radii of zonotopes, and apply our
algorithm to prove the first open case of three runners with individual
starting points.
