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2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (2006)
Berkeley, California
Oct. 21, 2006 to Oct. 24, 2006
ISSN: 0272-5428
ISBN: 0-7695-2720-5
pp: 449-458
Alexandr Andoni , M.I.T., USA
Piotr Indyk , M.I.T., USA
Mihai Patrascu , M.I.T., USA
ABSTRACT
We investigate the optimality of (1+\in )-approximation algorithms obtained via the dimensionality reduction method. We show that: <p>--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.</p> <p>--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)</p> <p>Both lower bounds are (essentially) tight.</p>
INDEX TERMS
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CITATION

P. Indyk, A. Andoni and M. Patrascu, "On the Optimality of the Dimensionality Reduction Method," 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)(FOCS), Berkeley, California, 2006, pp. 449-458.
doi:10.1109/FOCS.2006.56
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