Obliviously Approximating Sequence Distances

There are several applications for schemes which approximately nd the distance between two sequences in a way that isòblivious' of one of the sequences up until a nal sublinear number of comparisons. This paper shows how sequences can be preprocessed obliviously to give a binary string, so that a simple vector distance between two bitstrings gives an approximation to a sequence distance of interest. Small constant factor approximations are given for the Reversal, Transposition and Swap Distances, and a logarithmic factor approximation for Sequence Edit Distance which is analagous to Levenstein Edit Distance. By embedding these distances into vector distances (such as the Hamming metric) existing methods can then be used for the Approximate Nearest Neighbors and Clustering problems on these vector distances to solve the corresponding problems approximately for the sequence distances that are being embedded.