Uniquely Represented Data Structures for Computational Geometry
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
B-Treaps: A Uniquely Represented Alternative to B-Trees
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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We 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. We 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 $\Omega(n^{1/3})$. Therefore, our result sheds new light on previously claimed lower bounds for unique representation of dictionaries.