Faster uniquely represented dictionaries

The authors present a solution to the dictionary problem where each subset of size n of an ordered universe is represented by a unique structure, containing a (unique) binary search tree. The structure permits the execution of search, insert, and delete operations in O(n^1/3) time in the worst case. They also give a general lower bound, stating that for any unique representation of a set in a graph of, bounded outdegree, one of the operations search or update must require a cost of Ω(n ^1/3) Therefore, the result sheds new light on previously claimed lower bounds for unique binary search tree representations