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A Geometric Approach to Lower Bounds for Approximate Near-Neighbor Search and Partial Match

8 years 10 months ago
A Geometric Approach to Lower Bounds for Approximate Near-Neighbor Search and Partial Match
This work investigates a geometric approach to proving cell probe lower bounds for data structure problems. We consider the approximate nearest neighbor search problem on the Boolean hypercube ({0, 1}d , · 1) with d = Θ(log n). We show that any (randomized) data structure for the problem that answers c-approximate nearest neighbor search queries using t probes must use space n1+Ω(1/ct) . In particular, our bound implies that any data structure that uses space ˜O(n) with polylogarithmic word size, and with constant probability gives a constant approximation to nearest neighbor search queries must probe the data structure Ω(log n/ log log n) times. This improves on the lower bound of Ω(log log d/ log log log d) probes shown by Chakrabarti and Regev [8] for any polynomial space data structure, and the Ω(log log d) lower bound in P˘atra¸scu and Thorup [25] for linear space data structures. Our lower bound holds for the near neighbor problem, where the algorithm knows in advan...
Rina Panigrahy, Kunal Talwar, Udi Wieder
Added 29 May 2010
Updated 29 May 2010
Type Conference
Year 2008
Where FOCS
Authors Rina Panigrahy, Kunal Talwar, Udi Wieder
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