Before revision:  Given an acyclic inequality join between tables of size n , it returns the join answers in order and guarantees that for every value of k, the k top-ranked answers are returned in O(n polylog n + k log k) time . This matches  the best-known guarantee for equi-joins up to a polylogarithmic factor .
After revision:  Given an acyclic inequality join between tables of size n , it returns the join answers in order and guarantees that for every value of k, the k top-ranked answers are returned in O(n polylog n + k log k) time and \mathcal{O the best-known guarantee for equi-joins up to a polylogarithmic factor .