Methods in Algorithmic Analysis - Dobrushkin, Vladimir A.

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Auteur(s) : Dobrushkin, Vladimir A.

Editeur : Chapman And Hall/Crc

Langue : Anglais

Parution : 01/11/2009

Format : Moyen, de 350g à 1kg

Nombre de pages : 826

Expédition : 1617

Dimensions : 26.0 x 18.3 x 4.8

ISBN : 1420068296

Résumé :
Focusing on the analysis of algorithms, this book presents a comprehensive treatment of the mathematics used to analyze computer algorithms. It provides information on the theory of the topic by including many algorithms and code fragments with detailed analysis. Unlike similar books, this one contains material on enumeration with generating functions, shuffle products, combinatorics of strings, counting in regular languages, and asymptotics from recurrences. The text incorporates the use of C++ throughout and includes many examples and exercises of varying levels of difficulty. A solutions manual is available for qualifying instructors.

Biographie:

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.

Sommaire:
PRELIMINARIES Why Do We Analyze Algorithms? Proofs Iteration and Recursion COMBINATORICS Properties of Summation Multiple Sums Principles of Counting Permutations and Combinations Binomial Coefficients Binomial Coefficient and Hypergeometric Functions Stirling Approximation PROBABILITY Set Operations Sample Space and Random Variables Calculating Probabilities Random Variables Conditional Probabilities Independence Joint Distributions Dependent Random Variables MORE ABOUT PROBABILITY Special Distributions Types of Probabilistic Convergence The Theorem of Total Probability Bayes' Theorem Convolution Order Statistics Chebyshev Inequality Sundry Examples RECURRENCES OR DIFFERENCE EQUATIONS How Do Difference Equations Arise? Properties of Difference Equations First Order Linear Difference Equations Divide-and-Conquer Recurrences Quicksort Recurrence Recurrences in Numerical Analysis Continued Fractions Partial Difference Equations Some Applications INTRODUCTION TO GENERATING FUNCTIONS Generating Functions-Definitions Extraction of Coefficients Counting Binary Trees Solving Recurrences Snake Oil Summation Applications in Probability The Langrage Inversion Theorem ENUMERATION WITH GENERATING FUNCTIONS Definition of Enumerators Sum and Product Rules Counting Compositions of Integers Further Set Operations Partition of Integers Exponential Enumerators FURTHER ENUMERATION METHODS Enumeration of Trees Occupancy Enumeration The Principle of Inclusion and Exclusion (PIE) Extensions and Further Applications of the PIE Probabilistic Inclusion-Exclusion Principle Runs in Permutations Special Topics COMBINATORICS OF STRINGS Operations on Languages Regular Languages Counting Regular Languages Waiting Time Probabilistic Problems Algorithms and Markov Chains INTRODUCTION TO ASYMPTOTICS Asymptotic Notation and Applications The Critical Range Method Rice's Method The Euler Summation Formula Finding Primes Asymptotics from Recurrences Limit Laws in Probability ASYMPTOTICS AND GENERATING FUNCTIONS Elementary Bounds from Generating Functions Estimates from Singularities Estimates from Entire Functions Examples and Exercises REVIEW OF ANALYTIC TECHNIQUES Complex Numbers Review of Power Series Functions of a Complex Variable: Basic Concepts Differential Operators Partial Fraction Decomposition Some Special Functions Stieltjes Integrals APPENDICES BIBLIOGRAPHY ANSWERS/HINTS TO SELECTED PROBLEMS INDEX

...helpful to any mathematics student who wishes to acquire a background in classical probability and analysis ... This is a remarkably beautiful book that would be a pleasure for a student to read, or for a teacher to make into a year's course. -Harvey Cohn, Computing Reviews, May 2010