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Many emerging data mining applications require a similarity join between points in a high-dimensional domain. We present a new algorithm that utilizes a new index structure, called the epsilon-kdB tree, for fast spatial similarity joins on high-dimensional points. This index structure reduces the number of neighboring leaf nodes that are considered for the join test, as well as the traversal cost of finding appropriate branches in the internal nodes. The storage cost for internal nodes is independent of the number of dimensions. Hence the proposed index structure scales to high-dimensional data. Empirical evaluation, using synthetic and real-life datasets, shows that similarity join using the epsilon-kdB tree is 2 to an order of magnitude faster than the R+ tree, with the performance gap increasing with the number of dimensions.