## Abstract

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 x_{i} ≠ *, we have x_{i} = y_{i}. In this paper we show randomized lower bounds in the cell-probe model for this well-studied problem. Our lower bounds follow from a two-party asymmetric randomized communication complexity near-optimal lower bound for this problem, where we show that either Alice has to send Ω(d/log n) bits or Bob has to send Ω(n^{1-0(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 Ω(d/log^{2}n) probes are needed. This is an exponential improvement over the previously known lower bounds for this problem. Our lower bound also leads to new and improved lower bounds for related problems including a lower bound for the l_{∞} c-nearest neighbor problem for c < 3 and an improved communication complexity lower bound for the exact nearest neighbor problem.

Original language | American English |
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Pages (from-to) | 667-672 |

Number of pages | 6 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 2003 |

Externally published | Yes |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: 9 Jun 2003 → 11 Jun 2003 |

## Keywords

- Algorithms
- Theory