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Cet ouvrage presente les types d'arbres les plus utilises en informatique, sous les angles algorithmique et mathematique. Pour chaque type, nous donnons les algorithmes courants associes et des exemples d'utilisation, directe ou en modelisation, puis nous etudions leurs performances d'un point de vue mathematique. Nos outils sont les mathematiques discretes, les probabilites et la combinatoire analytique, presentes ici simultanement.Le public vise est d'abord celui des etudiants de niveau master scientifique ou en derniere annee d'ecole d'ingenieurs avec un cursus prealable en informatique ou en mathematiques, ou ceux visant une double competence en mathematiques et informatique ; ainsi que toute personne dotee d'un bagage scientifique
minimal
et amenee a utiliser des structures arborescentes liees a des algorithmes, qui souhaiterait avoir une meilleure connaissance de ces structures et une idee des performances des algorithmes associes sans se plonger dans les travaux originaux.
This book presents a wide range of tree structures, from both a computer science and a mathematical point of view. For each of these structures we give the algorithms that allow us to visit or update the structure, and discuss their potential uses, either directly (for storing data) or in modelling a variety of situations. We present a mathematical approach to their performances; this is done by the systematic and parallel use of tools from discrete mathematics, probability and analytic combinatorics.The book is intended for graduate students in mathematics or computer science (or both) and in engineering schools. It is also suitable for anyone with a basic level of scientific knowledge who may have to use tree structures and related algorithms, and who wishes to get a rigorous knowledge of their performance without going back to the original, often specialized, results.
