 Under mild conditions, we show that chasing algorithms with sufficient bounded speed approximate the optimal cost at every time step for oriented bounding boxes and strips , but not for principal components .
<clarity>  Under mild conditions, we show that chasing algorithms with sufficient bounded speed approximate the optimal cost at every time step for oriented bounding boxes and strips , but not for principal components .
 Under mild conditions, we show that chasing algorithms with sufficient bounded speed approximate the optimal cost at all times for oriented bounding boxes and strips , but not for principal components .