Cell-probe lower bounds for the partial match problem

T. S. Jayram*, Subhash Khot, Ravi Kumar, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations

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 xi ≠ *, we have xi = yi. 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(n1-0(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/log2n) 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 languageAmerican English
Pages (from-to)667-672
Number of pages6
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs
StatePublished - 2003
Externally publishedYes
Event35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: 9 Jun 200311 Jun 2003

Keywords

  • Algorithms
  • Theory

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