Methods in Algorithmic Analysis / by Vladimir A. Dobrushkin.

Methods in Algorithmic Analysis /

Explores the Impact of the Analysis of Algorithms on Many Areas within and beyond Computer ScienceA 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...

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Bibliographic Details
Main Author: Dobrushkin, Vladimir A. (Author)
Corporate Author: Taylor and Francis
Format: Electronic eBook
Language:English
Published: Boca Raton, FL : Taylor and Francis, an imprint of Chapman and Hall/CRC, [2011]
Edition:First edition.
Series:Chapman & Hall/CRC computer and information science series.
Subjects:
Algorithms.
Computer algorithms.
Computer science > Mathematics.
Electronic books.
Online Access: Full text (WIT users only)
Table of Contents:
  • 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 FunctionsDefinitions
  • 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
  • Rices 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.

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