Analysis of String Sorting using Heapsort

TL;DR

This thesis analyzes the complexity of string sorting using Heapsort, considering prefix trie structures and symbol comparisons, extending prior work on Quicksort and Mergesort to include Binomial heap implementations.

Contribution

It introduces a complexity analysis of Heapsort for string sorting within a trie-based model, including Binomial heap variants, expanding theoretical understanding.

Findings

Complexity expressed via prefix trie structures.

Extended analysis to Heapsort and Binomial heaps.

Provides bounds for classical algorithms in string sorting.

Abstract

In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation takes into account symbol comparisons and not just comparisons between the strings. The analysis of upper and lower bounds for some classical algorithms such as Quicksort and Mergesort in terms of such a model was shown. Here we extend the analysis to another classical algorithm - Heapsort. We also give analysis for the version of the algorithm that uses Binomial heaps as a heap implementation.