Introduction to the Design and Analysis of Algorithms

Anany Levitin (Autor)

Buch | Softcover

600 Seiten

2011 | 3rd edition
Pearson (Verlag)
978-0-13-231681-1 (ISBN)

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Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a coherent and innovative manner. Written in a student-friendly style, the book emphasizes the understanding of ideas over excessively formal treatment while thoroughly covering the material required in an introductory algorithms course. Popular puzzles are used to motivate students' interest and strengthen their skills in algorithmic problem solving. Other learning-enhancement features include chapter summaries, hints to the exercises, and a detailed solution manual.

Dr. Anany Levitin graduated from the Moscow State University with an MS degree in Mathematics. He holds a Ph.D. degree in Mathematics from the Hebrew University of Jerusalem and an MS degree in Computer Science from the University of Kentucky. Introduction to the Design and Analysis of Algorithms has been translated into Chinese, Russian, Greek, and Korean and is used in hundreds of schools all over the world. Dr. Levitin is also the author of Algorithmic Puzzles, publishing in Fall 2011. Dr. Levitin teaches courses in the Design and Analysis of Algorithms at Villanova University.

Table of Contents

New to the Third Edition
Preface

Introduction

1.1 What Is an Algorithm?

Exercises 1.1

1.2 Fundamentals of Algorithmic Problem Solving

Understanding the Problem
Ascertaining the Capabilities of the Computational Device
Choosing between Exact and Approximate Problem Solving
Algorithm Design Techniques
Designing an Algorithm and Data Structures
Methods of Specifying an Algorithm
Proving an Algorithm’s Correctness
Analyzing an Algorithm
Coding an Algorithm
Exercises 1.2

1.3 Important Problem Types

Sorting
Searching
String Processing
Graph Problems
Combinatorial Problems
Geometric Problems
Numerical Problems
Exercises 1.3

1.4 Fundamental Data Structures

Linear Data Structures
Graphs
Trees
Sets and Dictionaries
Exercises 1.4

Summary

Fundamentals of the Analysis of Algorithm Efficiency

2.1 The Analysis Framework

Measuring an Input’s Size
Units for Measuring Running Time
Orders of Growth
Worst-Case, Best-Case, and Average-Case Efficiencies
Recapitulation of the Analysis Framework
Exercises 2.1

2.2 Asymptotic Notations and Basic Efficiency Classes

Informal Introduction
O-notation
-notation
-notation
Useful Property Involving the Asymptotic Notations
Using Limits for Comparing Orders of Growth
Basic Efficiency Classes
Exercises 2.2

2.3 Mathematical Analysis of Nonrecursive Algorithms

Exercises 2.3

2.4 Mathematical Analysis of Recursive Algorithms

Exercises 2.4

2.5 Example: Computing the nth Fibonacci Number

Exercises 2.5

2.6 Empirical Analysis of Algorithms

Exercises 2.6

2.7 Algorithm Visualization

Summary

Brute Force and Exhaustive Search

3.1 Selection Sort and Bubble Sort

Selection Sort
Bubble Sort
Exercises 3.1

3.2 Sequential Search and Brute-Force String Matching

Sequential Search
Brute-Force String Matching
Exercises 3.2

3.3 Closest-Pair and Convex-Hull Problems by Brute Force

Closest-Pair Problem
Convex-Hull Problem
Exercises 3.3

3.4 Exhaustive Search

Traveling Salesman Problem
Knapsack Problem
Assignment Problem
Exercises 3.4

3.5 Depth-First Search and Breadth-First Search

Depth-First Search
Breadth-First Search
Exercises 3.5

Summary

Decrease-and-Conquer

4.1 Insertion Sort

Exercises 4.1

4.2 Topological Sorting

Exercises 4.2

4.3 Algorithms for Generating Combinatorial Objects

Generating Permutations
Generating Subsets
Exercises 4.3

4.4 Decrease-by-a-Constant-Factor Algorithms

Binary Search
Fake-Coin Problem
Russian Peasant Multiplication
Josephus Problem
Exercises 4.4

4.5 Variable-Size-Decrease Algorithms

Computing a Median and the Selection Problem
Interpolation Search
Searching and Insertion in a Binary Search Tree
The Game of Nim
Exercises 4.5

Summary

Divide-and-Conquer

5.1 Mergesort

Exercises 5.1

5.2 Quicksort

Exercises 5.2

5.3 Binary Tree Traversals and Related Properties

Exercises 5.3

5.4 Multiplication of Large Integers and Strassen’s Matrix Multiplication

Multiplication of Large Integers
Strassen’s Matrix Multiplication
Exercises 5.4

5.5 The Closest-Pair and Convex-Hull Problems

by Divide-and-Conquer
The Closest-Pair Problem
Convex-Hull Problem
Exercises 5.5

Summary

Transform-and-Conquer

6.1 Presorting

Exercises 6.1

6.2 Gaussian Elimination

LU Decomposition
Computing a Matrix Inverse
Computing a Determinant
Exercises 6.2

6.3 Balanced Search Trees

AVL Trees
2-3 Trees
Exercises 6.3

6.4 Heaps and Heapsort

Notion of the Heap
Heapsort
Exercises 6.4

6.5 Horner’s Rule and Binary Exponentiation

Horner’s Rule
Binary Exponentiation
Exercises 6.5

6.6 Problem Reduction

Computing the Least Common Multiple
Counting Paths in a Graph
Reduction of Optimization Problems
Linear Programming
Reduction to Graph Problems
Exercises 6.6

Summary

Space and Time Trade-Offs

7.1 Sorting by Counting

Exercises 7.1

7.2 Input Enhancement in String Matching

Horspool’s Algorithm
Boyer-Moore Algorithm
Exercises 7.2

7.3 Hashing

Open Hashing (Separate Chaining)
Closed Hashing (Open Addressing)
Exercises 7.3

7.4 B-Trees

Exercises 7.4

Summary

Dynamic Programming

8.1 Three Basic Examples

Exercises 8.1

8.2 The Knapsack Problem and Memory Functions

Memory Functions
Exercises 8.2

8.3 Optimal Binary Search Trees

Exercises 8.3

8.4 Warshall’s and Floyd’s Algorithms

Warshall’s Algorithm
Floyd’s Algorithm for the All-Pairs Shortest-Paths Problem
Exercises 8.4

Summary

Greedy Technique

9.1 Prim’s Algorithm

Exercises 9.1

9.2 Kruskal’s Algorithm

Disjoint Subsets and Union-Find Algorithms
Exercises 9.2

9.3 Dijkstra’s Algorithm

Exercises 9.3

9.4 Huffman Trees and Codes

Exercises 9.4

Summary

Iterative Improvement

10.1 The Simplex Method

Geometric Interpretation of Linear Programming
An Outline of the Simplex Method
Further Notes on the Simplex Method
Exercises 10.1

10.2 The Maximum-Flow Problem

Exercises 10.2

10.3 Maximum Matching in Bipartite Graphs

Exercises 10.3

10.4 The Stable Marriage Problem

Exercises 10.4

Summary

Limitations of Algorithm Power

11.1 Lower-Bound Arguments

Trivial Lower Bounds
Information-Theoretic Arguments
Adversary Arguments
Problem Reduction
Exercises 11.1

11.2 Decision Trees

Decision Trees for Sorting
Decision Trees for Searching a Sorted Array
Exercises 11.2

11.3 P, NP, and NP-Complete Problems

P and NP Problems
NP-Complete Problems
Exercises 11.3

11.4 Challenges of Numerical Algorithms

Exercises 11.4

Summary

Coping with the Limitations of Algorithm Power

12.1 Backtracking

n-Queens Problem
Hamiltonian Circuit Problem
Subset-Sum Problem
General Remarks
Exercises 12.1

12.2 Branch-and-Bound

Assignment Problem
Knapsack Problem
Traveling Salesman Problem
Exercises 12.2

12.3 Approximation Algorithms for NP-Hard Problems

Approximation Algorithms for the Traveling Salesman Problem
Approximation Algorithms for the Knapsack Problem
Exercises 12.3

12.4 Algorithms for Solving Nonlinear Equations

Bisection Method
Method of False Position
Newton’s Method
Exercises 12.4

Summary
Epilogue

APPENDIX A

Useful Formulas for the Analysis of Algorithms
Properties of Logarithms
Combinatorics
Important Summation Formulas
Sum Manipulation Rules
Approximation of a Sum by a Definite Integral
Floor and Ceiling Formulas
Miscellaneous

APPENDIX B

Short Tutorial on Recurrence Relations
Sequences and Recurrence Relations
Methods for Solving Recurrence Relations
Common Recurrence Types in Algorithm Analysis

References Hints to Exercises Index

Erscheint lt. Verlag	29.12.2011
Sprache	englisch
Maße	10 x 10 mm
Gewicht	750 g
Themenwelt	Informatik ► Theorie / Studium ► Algorithmen
ISBN-10	0-13-231681-1 / 0132316811
ISBN-13	978-0-13-231681-1 / 9780132316811
Zustand	Neuware