Tighter bounds for nearest neighbor search and related problems in the cell probe model

Omer Barkol, Yuval Rabani

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

26 Scopus citations

Abstract

We prove new lower bounds for nearest neighbor search in the Hamming cube. Our lower bounds are for randomized, two-sided error, algorithms in Yao's cell probe model. Our bounds are in the form of a tradeoff among the number of cells, the size of a cell, and the search time. For example, suppose we are searching among n points in the d dimensional cube, we use poly(n, d) cells, each containing poly(d, log n) bits. We get a lower bound of Ω(d/log n) on the search time, a significant improvement over the recent bound of Ω(log d) of Borodin et al. This should be contrasted with the upper bound of O(log log d) for approximate search (and O(1) for a decision version of the problem; our lower bounds hold in that case). By previous results, the bounds for the cube imply similar bounds for nearest neighbor search in high dimensional Euclidean space, and for other geometric problems.

Original languageAmerican English
Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Pages388-396
Number of pages9
DOIs
StatePublished - 2000
Externally publishedYes
Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
Duration: 21 May 200023 May 2000

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Country/TerritoryUnited States
CityPortland, OR
Period21/05/0023/05/00

Bibliographical note

Funding Information:
1Work partially supported by the Milton and Lillian Edwards Fellowship. 2This work was supported by Grant 386/99-1 of the Israel Science Foundation founded by the Israeli Academy of Sciences and Humanities, by the N. Haar and R. Zinn Research Fund, and by the Fund for the Promotion of Research at the Technion.

Fingerprint

Dive into the research topics of 'Tighter bounds for nearest neighbor search and related problems in the cell probe model'. Together they form a unique fingerprint.

Cite this