While the ideas used in disjoint-set forests have long been familiar, [[Robert Tarjan]] was the first to prove the upper bound (and a restricted version of the lower bound) in terms of the inverse AckmannAckermann function. Until this time the best bound on the time per operation, proven by Hopcroft and Ullman, was O(log<sup>*</sup> n), the [[iterated logarithm]] of n, another slowly-growing function (but not quite as slow as the inverse AckmannAckermann function). Tarjan and van Leeuwen also developed one-pass ''Find'' algorithms that are more efficient in practice. The algorithm was made well-known by the popular textbook ''Introduction to Algorithms'', listed in the references.
