A Fiat-Naor-based inversion technique yields data structures for range searching, counting, and related queries on implicit sets f([N]) with ~O(N^{1-α/3}) space and ~O(N^α) query time for any α ∈ (0,1).
Kane, Shachar Lovett, and Shay Moran
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A General Technique for Searching in Implicit Sets via Function Inversion
A Fiat-Naor-based inversion technique yields data structures for range searching, counting, and related queries on implicit sets f([N]) with ~O(N^{1-α/3}) space and ~O(N^α) query time for any α ∈ (0,1).