Cell-probe lower bounds for the partial match problem

Given a database of n points in {0, 1}d, the partial match problem is: In response to a query x in {0, 1, }d, find a database point y such that for every i whenever xi = , we have xi = yi. In this paper we show randomized lower bounds in the cell-probe model for this well-studied problem [Riv74, Knu73, Riv76, MNSW98, BOR99, CIP02]. Our lower bounds follow from a two-player asymmetric randomized communication complexity near-optimal lower bound for this problem, where we show that either Alice has to send (d/ log n) bits or Bob has to send (n1-o(1)) bits. When applied to the cell-probe model, it means that if the number of cells is restricted to be poly(n, d) where each cell is of size poly(log n, d), then (d/ log2 n) probes are needed. This is an exponential improvement over the previously known lower bounds for this problem obtained by Miltersen et al. [MNSW98] and Borodin et al. [BOR99]. Our lower bound also leads to new and improved lower bounds for related problems including a low...

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: T. S. Jayram, Subhash Khot, Ravi Kumar, Yuval Rabani
• Keywords: Algorithms, Et Al, Exact Nearest Neighbor, Lower Bounds, STOC 2003