On the Optimality of the Dimensionality Reduction Method

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 nΩ(1/ 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.

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: Alexandr Andoni, Piotr Indyk, Mihai Patrascu
• Keywords: Closest Substring Problem, Dimensionality Reduction Method, FOCS 2006, Nearest Neighbor Problem, Theoretical Computer Science