We consider the approximate nearest neighbour search problem on the
Hamming Cube $\b^d$. We show that a randomised cell probe algorithm that
uses polynomial storage and word size $d^{O(1)}$ requires a worst case
query time of $\Omega(\log\log d/\log\log\log d)$. The approximation
factor may be as loose as $2^{\log^{1-\eta}d}$ for any ... more >>>

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic \emph{boolean} (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.

We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a $\tilde{\Omega}(\log^{1.5} ... more >>>

We construct an explicit distribution $\mathbf{D}$ over $\{0,1\}^N$ that exhibits an essentially optimal separation between adaptive and non-adaptive cell-probe sampling. The distribution can be sampled exactly when each output bit is allowed two adaptive probes to an arbitrarily long sequence of independent uniform symbols from $[N]$. In contrast, any non-adaptive ... more >>>