We prove an Ω(dlgn/(lglgn)2) lower bound on the dynamic
cell-probe complexity of statistically oblivious
approximate-near-neighbor search (ANN) over the d-dimensional
Hamming cube. For the natural setting of d=Θ(logn), our result
implies an Ω~(lg2n) lower bound, which is a quadratic
improvement over the highest (non-oblivious) cell-probe lower bound for
ANN. This is the first super-logarithmic unconditional
lower bound for ANN against general (non black-box) data structures.
We also show that any oblivious static data structure for
decomposable search problems (like ANN) can be obliviously dynamized
with O(logn) overhead in update and query time, strengthening a classic
result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page