In this paper, we propose an approximate solution to the multi-step k-NN search. The traditional multi-step k-NN search (1) determines a tolerance through a k-NN query on a multidimensional index and (2) retrieves the final k results by evaluating the tolerance-based range query on the index and by accessing the actual database. The proposed tolerance reduction-based (approximate) solution reduces a large number of candidates by adjusting the tolerance of the range query on the index. To obtain the tight tolerance, the proposed solution forcibly decreases the tolerance by the average ratio of high-dimensional and low-dimensional distances. Experimental results show that the proposed approximate solution significantly reduces the number of candidates and the k-NN search time over the existing one.
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