Methods in Algorithmic Analysis Chapman & Hall/CRC Computer and Information Science Series
Auteur : Dobrushkin Vladimir A.
Explores the Impact of the Analysis of Algorithms on Many Areas within and beyond Computer Science
A flexible, interactive teaching format enhanced by a large selection of examples and exercises
Developed from the author?s own graduate-level course, Methods in Algorithmic Analysis presents numerous theories, techniques, and methods used for analyzing algorithms. It exposes students to mathematical techniques and methods that are practical and relevant to theoretical aspects of computer science.
After introducing basic mathematical and combinatorial methods, the text focuses on various aspects of probability, including finite sets, random variables, distributions, Bayes? theorem, and Chebyshev inequality. It explores the role of recurrences in computer science, numerical analysis, engineering, and discrete mathematics applications. The author then describes the powerful tool of generating functions, which is demonstrated in enumeration problems, such as probabilistic algorithms, compositions and partitions of integers, and shuffling. He also discusses the symbolic method, the principle of inclusion and exclusion, and its applications. The book goes on to show how strings can be manipulated and counted, how the finite state machine and Markov chains can help solve probabilistic and combinatorial problems, how to derive asymptotic results, and how convergence and singularities play leading roles in deducing asymptotic information from generating functions. The final chapter presents the definitions and properties of the mathematical infrastructure needed to accommodate generating functions.
Accompanied by more than 1,000 examples and exercises, this comprehensive, classroom-tested text develops students? understanding of the mathematical methodology behind the analysis of algorithms. It emphasizes the important relation between continuous (classical) mathematics and discrete mathematics, which is the basis of computer science.
Preliminaries. Combinatorics. Probability. More about Probability. Recurrences or Difference Equations. Introduction to Generating Functions. Enumeration with Generating Functions. Further Enumeration Methods. Combinatorics of Strings. Introduction to Asymptotics. Asymptotics and Generating Functions. Review of Analytic Techniques. Appendices. Bibliography. Answers/Hints to Selected Problems. Index.
Vladimir A. Dobrushkin is a professor in the Division of Applied Mathematics at Brown University and a professor in the Department of Computer Science at Worcester Polytechnic Institute.
Date de parution : 06-2017
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 14 jours).
Prix indicatif 93,24 €
Ajouter au panierDate de parution : 11-2009
Ouvrage de 608 p.
17.8x25.4 cm
Thèmes de Methods in Algorithmic Analysis :
Mots-clés :
Exponential Generating Function; Vladimir Dobrushkin; Binomial Coefficients; Combinatorial Preliminaries; Euler Summation Formula; Probability; Ordinary Generating Functions; analysis of algorithms; Random Variable; computer algorithms; Cumulative Distribution Function; Chapman & Hall/CRC Computer and Information Science; Fibonacci Numbers; Chebyshev inequality; Kleene Closure; Bayes' theorem; Stirling Numbers; Markov chains; Binary Tree; numerous theories; Power Series; algorithmic analysis; Indicator Random Variables; Generating Function; BST; AVL Tree; Partial Difference Equations; Discrete Random Variables; Difference Equation; Asymptotic Expansion; Partial Fraction; Binomial Theorem; Distribution Function; Summation Formula; P1 P2; Probability Generating Function