When processing m i , it takes each partial partition P P in H i−1 and creates a set of ith-order partitions by extending P P with m i in all possible ways.
for each cluster C (formed by a subset of the first i-1 mentions) in P P , the algorithm generates a new ith-order partition, P P ′ , by linking m i to C (line 9), and stores P P ′ in H i (line 11).