  We consider a variant of Cops and Robbers in which the robber may traverse as
many edges as he likes in each turn, with the constraint that he cannot pass
through any vertex occupied by a cop. We study this model on several classes of
grid-like graphs. In particular, we determine the cop numbers for
two-dimensional Cartesian grids and tori up to an additive constant, and we
give asymptotic bounds for the cop numbers of higher-dimensional grids and
hypercubes.
