E cient Search for Approximate Nearest Neighbor in High Dimensional Spaces

We address the problem of designing data structures that allow e cient search for approximate nearest neighbors. More speci cally, given a database consisting of a set of vectors in some high dimensional Euclidean space, we want to construct a space-e cient 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. Signi cantly 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). Computer Science Department, Technion | IIT, Haifa 32000, Israel. Email: [email protected] yBell Communications Research, MCC-1C365B, 445 South Street, Morristown, NJ 07960-6438, USA. Email: [email protected] zComputer Science Department, Technion | IIT, Haifa 32000, Israel. Part of this work was done while visiting Bell Communications Research. Work at the Technion supported by BSF grant 96-00402, by a David and Ruth Moskowitz Academic Lecturship award, and by grants from the S. and N. Grand Research Fund, from the Smoler Research Fund, and from the Fund for the Promotion of Research at the Technion. Email: [email protected]