Optimal multi-step k-nearest neighbor search

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Abstract
For an increasing number of modern database applications, efficient support of similarity search becomes an important task. Along with the complexity of the objects such as images, molecules and mechanical parts, also the complexity of the similarity models increases more and more. Whereas algorithms that are directly based on indexes work well for simple medium-dimensional similarity distance functions, they do not meet the efficiency requirements of complex high-dimensional and adaptable distance functions. The use of a multi-step query processing strategy is recommended in these cases, and our investigations substantiate that the number of candidates which are produced in the filter step and exactly evaluated in the refinement step is a fundamental efficiency parameter. After revealing the strong performance shortcomings of the state-of-the-art algorithm for k -nearest neighbor search [Korn et al. 1996], we present a novel multi-step algorithm which is guaranteed to produce the minimum number of candidates. Experimental evaluations demonstrate the significant performance gain over the previous solution, and we observed average improvement factors of up to 120 for the number of candidates and up to 48 for the total runtime.

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