Fusion Tree Sorting

The sorting problem is one of the most relevant problems in computer science. Within the scope of modern computer science it has been studied for more than 70 years. In spite of these facts, new sorting algorithms have been developed in recent years. Among several types of sorting algorithms, some are quicker; others are more economic in relation to space, whereas others insert a few restrictions in relation to data input. This paper is aimed at explaining the fusion tree data structure, which is responsible for the first sorting algorithm with complexity time smaller than nlgn. The nlgn time complexity has led to some confusion and generated the wrong belief in part of the community of being the minimum possible for this type of problem.Comment: 17 page

Performance of the Ultra-Wide Word Model

The Ultra-wide word model of computation (UWRAM) is an extension of the Word-RAM model which has an ALU that can operate on w^2 bits at a time, where w is the size in bits of a cell in memory. The purpose of this thesis is to explore the applicability of the UWRAM model, particularly when compared to the PRAM model, from an algorithmic point of view, to determine its potential for common applications. The work is divided into three sections: First we describe the model, its instruction set, strengths and weaknesses, and provide a few small examples that showcase the functionality of the model and how simple techniques can be used to speed up sequential algorithms. In the second section, we discuss the problem of sorting and searching, and show that elaborate data structures such as the fusion tree can be easily adapted to the model, allowing the sorting of n integers in O(n (log n/log log n) time with small constant factors. Lastly, we provide simulations of UWRAM and PRAM programs to solve two problems: subset sum and string matching. In the first case we show how a dynamic programming algorithm can be sped up using bit parallelism where traditional parallelism is difficult to achieve, and in the second, we show that even in a problem that is simple to parallelize traditionally, the UWRAM can perform well when compared to a PRAM