A Cost Model for Nearest Neighbor Search in High-Dimensional Data Space

Abstract

In this paper, we present a new cost model for nearest neighbor search in high-dimensional data space. We first analyze different nearest neighbor algorithms, present a generalization of an algorithm which has been originally proposed for Quadtrees [13], and show that this algorithm is optimal. Then, we develop a cost model which - in contrast to previous models - takes boundary effects into account and therefore also works in high dimensions. The advantages of our model are in particular: Our model works for data sets with an arbitrary number of dimensions and an arbitrary number of data points, is applicable to different data distributions and index structures, and provides accurate estimates of the expected query execution time. To show the practical relevance and accuracy of our model, we perform a detailed analysis using synthetic and real data. The results of applying our model to Hilbert and X-tree indices show that it provides a good estimation of the query performance, which is considerably better than the estimates by previous models especially for highdimensional data.