can now generate all pairs $i,j$ for which $x_i^\pi$ is present in both their sketches. From these we can compute, for each pair $i,j$ with non-zero sketch overlap, a count of the number of $x_i^\pi$ values they have in common. By applying a preset threshold, we know which pairs $i,j$ have heavily overlapping sketches. For instance, if the threshold were 80%, we would need the count to be at least 160 for any $i,j$. As we identify such pairs, we run the union-find to group documents into near-duplicate ``syntactic clusters''. This is essentially a variant of the single-link clustering algorithm introduced in Section 17.2 (page [*]).