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...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Rina Panigrahy, Kunal Talwar, Udi Wieder
• Keywords: Data Structures, FOCS 2008, Lower Bound, Nearest Neighbor, Theoretical Computer Science