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

Orner Barkol*, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 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 u) 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
Pages (from-to)873-896
Number of pages24
JournalJournal of Computer and System Sciences
Volume64
Issue number4
DOIs
StatePublished - 2002
Externally publishedYes

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.

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