Approximate Text Searching

This thesis focuses on the problem of text retrieval allowing errors, also called \approximate " string matching. The problem is to nd a pattern in a text, where the pattern and the text may have \errors". This problem has received a lot of attention in recent years because of its applications in many areas, such as information retrieval, computational biology and signal processing, to name a few. The aim of this work is the development and analysis of novel algorithms to deal with the problem under various conditions, as well as a better understanding of the problem itself and its statistical behavior. Although our results are valid in many dierent areas, we focus our attention on typical text searching for information retrieval applications. This makes some ranges of values for the parameters of the problem more interesting than others. We have divided this presentation in two parts. The rst one deals with on-line approximate string matching, i.e. when there is no time or space to preprocess the text. These algorithms are the core of o-line algorithms as well. On-line searching is the area of the problem where better algorithms existed. We have obtained new bounds for the probability of an approximate match of a pattern i