Linearity in directory growth of the multilevel grid file

Abstract

The multilevel grid file (MLGF) is a multidimensional dynamic hashed file organization. Asymptotic directory growth, defined as the growth of the directory as the data file expands, is an important factor for evaluating storage overhead of a multidimensional dynamic file organization. In this article we implement the MLGF and examine the growth of its directory. The concepts and the architecture of the MLGF were introduced in refs [1,2]. We argue that the asymptotic directory growth of the MLGF is linearly dependent on the growth of the data file regardless of data distributions, data skew, or correlation among different organizing attributes. To justify this argument, we perform extensive experiments with various distributions of data: uniform, normal, and exponential distributions. We further perform experiments for more complicated cases where the distributions are highly-skewed or highly-correlated. The results show that the directory size of the MLGF increases linearly in the number of records independently of data distributions, data skew, or correlation, and the rates of increase are nearly constant in all cases. The results also show that both of the blocking factor and number of dimensions do not affect the linearity in directory growth of the MLGF. Such characteristics are important advantages of the MLGF in comparison with other multidimensional file organizations in that storage requirement for the directory is minimized, and splitting, merging, and hyperplane search operations are made easier.