Efficient search for approximate nearest neighbor in high dimensional spaces

Eyal Kushilevitz*, Rafail Ostrovsky, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

190 Scopus citations


We address the problem of designing data structures that allow efficient search for approximate nearest neighbors. More specifically, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a space-efficient data structure that would allow us to search, given a query vector, for the closest or nearly closest vector in the database. We also address this problem when distances are measured by the L1 norm and in the Hamming cube. Significantly improving and extending recent results of Kleinberg, we construct data structures whose size is polynomial in the size of the database and search algorithms that run in time nearly linear or nearly quadratic in the dimension. (Depending on the case, the extra factors are polylogarithmic in the size of the database.)

Original languageAmerican English
Pages (from-to)457-474
Number of pages18
JournalSIAM Journal on Computing
Issue number2
StatePublished - 2000
Externally publishedYes


  • Data structures
  • Nearest neighbor search
  • Random projections


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