Storing these functions in two arrays that map each item number to its function value takes space formula_105, and this information is sufficient to determine the clustering itself. As Sibson shows, when a new item is added to the set of items, the updated functions representing the new single-linkage clustering for the augmented set, represented in the same way, can be constructed from the old clustering in time formula_105. The SLINK algorithm then loops over the items, one by one, adding them to the representation of the clustering.