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A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space -where k is logarithmic in n and independent of d -so that all pairwise distances are maintained within an arbitrarily small factor. All known constructions of such embeddings involve projecting the n points onto a random k-dimensional hyperplane. We give a novel construction of the embedding, suitable for database applications, whichdoi:10.1145/375551.375608 dblp:conf/pods/Achlioptas01 fatcat:yx5rbynspbdcjcfuotchmc5qam