Arbres Pour l'Algorithmique
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Cet ouvrage pr�sente les types d'arbres les plus utilis�s en informatique, sous les angles algorithmique et math�matique. Pour chaque type, nous donnons les algorithmes courants associ�s et des exemples d'utilisation, directe ou en mod�lisation, puis nous �tudions leurs performances d'un point de vue math�matique. Nos outils sont les math�matiques discr�tes, les probabilit�s et la combinatoire analytique, pr�sent�s ici simultan�ment.Le public vis� est d'abord celui des �tudiants de niveau master scientifique ou en derni�re ann�e d'�cole d'ing�nieurs avec un cursus pr�alable en informatique ou en math�matiques, ou ceux visant une double comp�tence en math�matiques et informatique; ainsi que toute personne dot�e d'un bagage scientifique minimal et amen�e � utiliser des structures arborescentes li�es � des algorithmes, qui souhaiterait avoir une meilleure connaissance de ces structures et une id�e des performances des algorithmes associ�s 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.
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