A New Trade-Off for Deterministic Dictionaries

We consider dictionaries over the universe U = {0; 1}w on a unit-cost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n)O(1) and updates in time (log n)O(1), where n is the size of the set stored. This is the first such data structure to simultaneously achieve query time (log n)o(1) and update time O(2(log n)c) for a constant c < 1.

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