Analysis of Insertion Costs in Priority Trees

Abstract

Priority trees are a data structure used for priority queue administration. Under the model that all permutations of the numbers 1, . . ., n are equally likely to construct a priority tree of size n we give a detailed average-case analysis of insertion cost measures: we study the recursion depth and the number of key comparisons when inserting an element into a random size-n priority tree. For inserting a random element we obtain exact and asymptotic results for the expectation and the variance and can further show a central limit law of the parameters studied and for inserting an element with specified priority we can show exact and asymptotic results for the expectation of these quantities.