Before revision:  Given a convex body , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from ) -- if none of the query points hits , then contains less than an -fraction of the input points.
After revision:  Given a convex body , via a separation oracle, the algorithm performs a small sequence of (oracle) stabbing queries (computed from  , then contains less than an -fraction of the input points.