Polynomially small redundancy for small-value augmented retrieval

Determine whether augmented retrieval with value domain size V = n^{o(1)} (including the case where V is a power of two) admits constant-time queries with polynomially small redundancy n^{1−Ω(1)}.

Background

The paper introduces augmented retrieval, showing that when an array of augmented queries is stored alongside retrieval, the redundancy can be reduced dramatically for large value universes (e.g., V ≥ n^{3+O(1)}), with constant-time queries and near-optimal space.

For smaller V, the provided constructions either require larger redundancy or additional randomness assumptions. The authors explicitly pose whether polynomially small redundancy remains achievable when V is subpolynomial in n, which would require new algorithmic ideas beyond those developed in the paper.