We investigate the optimality of (1+ )-approximation algorithms obtained via the dimensionality reduction method. We show that: • Any data structure for the (1 + )-approximate nearest neighbor problem in Hamming space, which uses constant number of probes to answer each query, must use n 2 ) space. • Any algorithm for the (1 + )-approximate closest substring problem must run in time exponential in 1/ 2−γ for any γ > 0 (unless 3SAT can be solved in subexponential time) Both lower bounds are (essentially) tight.
Andoni, Indyk and Pȃtraşcu REF show that for small > 0, any O(1)-probe algorithm for (1 + )-approximate near neighbor problem must use space n Ω( 1 2 ) .
On the Optimality of the Dimensionality Reduction Method
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
Mathematics Computer Science