Grid file algorithms: An analysis in the biased case

Abstract

Multi-key access to records in a dynamically growing file may be performed using grid file algorithms[7]. We specify two of them, that generalize mono-dimensional dynamic hashing. Then, we derive the average sizes of the associated directories and provide an asymptotic analysis for uniform and biased distributions. The growth of the indexes is non linear; for uniform distributions, sizes are: $O(n^{1 + \tfrac{1}{b}} )$or $O(n^{1 + \tfrac{{s - 1}}{{sb + 1}}} )$, where s is the number of attributes being used, n the file size, and b the page capacity of the system. At last, we compare exact values and asymptotics and study the robustness of grid file algorithms with respect to the bias of the distribution.