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The approximate string matching is a fundamental and recurrent problem thatarises in most computer science fields. This problem can be defined as follows:  Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet$\Sigma$, let $q$ be a query defined also on $\Sigma$, and let $k$ be apositive integer. We want to build a data structure on $D$ capable of answeringthe following query: find all words in $D$ that are at most different from thequery word $q$ with $k$ errors.  In this thesis, we study the approximate string matching methods indictionaries, texts, and indexes, to propose practical methods that solve thisproblem efficiently. We explore this problem in three complementary directions:  1) The approximate string matching in the dictionary. We propose twosolutions to this problem, the first one uses hash tables for $k \geq 2$, thesecond uses the Trie and reverse Trie, and it is restricted to (k = 1). The twosolutions are adaptable, without loss of performance, to the approximate stringmatching in a text.  2) The approximate string matching for \textit{autocompletion}, which is,find all suffixes of a given prefix that may contain errors. We give a newsolution better in practice than all the previous proposed solutions.  3) The problem of the alignment of biological sequences can be interpreted asan approximate string matching problem. We propose a solution for peers andmultiple sequences alignment.  \medskip All the results obtained showed that our algorithms, give the bestperformance on sets of practical data (benchmark from the real world). All ourmethods are proposed as libraries, and they are published online.

Approximate String Matching: Theory and Applications (La Recherche Approch\'ee de Motifs : Th\'eorie et Applications)