A Model for k-Nearest Neighbor Query Cost in Multidimensional Index Structures

The k-nearest neighbor query in multidimensional index structures is one of the most frequently used query types in multimedia databases and geographic information systems. Until now, most of the analytic models are restricted to a particular type of the index structure, for example, the R-Tree and they concentrate on the analysis of the range query. Recently, a cost model [3] was reported for nearest neighbor queries. However, the model considered only 1-nearest neighbor queries rather than k-nearest neighbor queries. In this paper, we present an analytic model for the cost of the k-nearest neighbor query in multidimensional index structures. As a basis of the model, we introduce the concept of the regional average volume and the varying density function. The advantages of our model are in particular as follows: It is applicable to any type of datasets with arbitrary distributions (uniform and non-uniform ones), works for the kas well as 1nearest neighbor query, and is a dynamic analysis method which enables a rapid analysis without requiring a time-consuming simulation of data. To estimate the accuracy of our model, we conducted a various range of experiments on the datasets with various distributions. The results show that our analytic model is accurate for the data sets with non-uniform distributions as well as uniform distributions in low and mid dimensions.