A population analysis for hierarchical data structures

Abstract

A new method termed population analysis is presented for approximating the distribution of node occupancies in hierarchical data structures which store a variable number of geometric data items per node. The basic idea is to describe a dynamic data structure as a set of populations which are permitted to transform into one another according to certain rules. The transformation rules are used to obtain a set of equations describing a population distribution which is stable under insertion of additional information into the structure. These equations can then be solved, either analytically or numerically, to obtain the population distribution. Hierarchical data structures are modeled by letting each population represent the nodes of a given occupancy. A detailed analysis of quadtree data structures for storing point data is presented, and the results are compared to experimental data. Two phenomena referred to as aging and phasing are defined and shown to account for the differences between the experimental results and those predicted by the model. The population technique is compared with statistical methods of analyzing similar data structures.