--Any data structure for the (1+\in )-approximate nearest neighbor problem in Hamming space, which uses constant number of probes to answer each query, must use n^{\Omega \left( {1/ \in ^2 } \right)} space.

--Any algorithm for the (1+\in )-approximate closest substring problem must run in time exponential in 1/ \in ^{2 - \gamma } for any \gamma > 0 (unless 3SAT can be solved in subexponential time)

Both lower bounds are (essentially) tight.