Cost Analysis of the Prefix Tree Data Structure

The data tree is a very widely used data structure in many application areas. The tree structure provides an efficient storage and data manipulation for different data lists or data sets. The prefix tree is a special tree structure to store ordered lists of data elements. In the prefix tree, the lists with common prefix part share the same path. As the prefix tree can be involved in many data manipulation algorithms, the cost estimation of the tree is an important component in the cost function of the whole data manipulation algorithm. This paper provides a cost analysis related to the tree size for a random input set of object lists. The analysis includes both analytical and simulation methods and the main result presented in this paper is an approximation function based on the gamma-distribution.