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We present a multi-dimensional indexing approach for fast sequence similarity search in DNA and protein databases. In particular, we propose effective transformations of subsequences into numerical vector domains and build efficient index structures on the transformed vectors. We then define distance functions in the transformed domain and examine properties of these functions. We experimentally compared their (a) approximation quality for k-Nearest Neighbor (k-NN) queries, (b) pruning ability and (c) approximation quality for E-range queries. Results for k-NN queries, which we present here, show that our proposed distances FD2 and WD2 (i.e. Frequency and Wavelet Distance functions for 2-grams) perform significantly better than the others. We then develop effective index structures, based on R-trees and scalar quantization, on top of transformed vectors and distance functions. Promising results from the experiments on real biosequence data sets are presented.