Lower Bounds for Oblivious Near-Neighbor Search [article]

Kasper Green Larsen and Tal Malkin and Omri Weinstein and Kevin Yeo
2019 arXiv   pre-print
We prove an Ω(d n/ ( n)^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( n), our result implies an Ω̃(^2 n) 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
more » ... oblivious static data structure for decomposable search problems (like ANN) can be obliviously dynamized with O( n) overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).
arXiv:1904.04828v1 fatcat:r3hafauyw5cuhfdvsejv3narsm