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 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.

我们研究确定有理多面体的覆盖半径的计算问题。该参数定义为相应膨胀多面体的晶格平移以覆盖整个空间所需的最小膨胀因子。作为我们的主要结果，我们描述了一种新的算法来解决这个问题，它比 Kannan (1992) 的唯一先验算法更简单、更有效且更容易实现。

受著名的孤独赛跑者猜想的一个变体的启发，我们使用它的几何解释来描述 zonotopes 的覆盖半径，并应用我们的算法来证明三个具有单独起点的赛跑者的第一个开放案例。