Foundations of Algorithms, Fourth Edition | by Richard Neapolitan and Kumarss Naimipour | 2011 | ISBN: 9780763782504. How to Develop Efficient Algorithms to solve Computational Complexity. Parallel Algorithms Model.

December 9th, 2010 | by kutenk |

Foundations of Algorithms, Fourth Edition
by Richard Neapolitan and Kumarss Naimipour
2011 (646 pages)
ISBN:9780763782504
Presenting mathematical concepts using standard English and a simpler notation than is found in most texts, this volume offers a well-balanced presentation of algorithm design, complexity analysis of algorithms, and computational complexity.




Foundation of Algorithms, Fourth Edition
Preface
Overview
Prerequisites
Chapter Contents
Pedagogy
Course Outlines
Instructor Resources
Acknowledgments
Errors

Chapter 1 – Algorithms: Efficiency, Analysis, and Order
Overview
1.1: Algorithms
1.2: The Importance of Developing Efficient Algorithms
1.3: Analysis of Algorithms
1.4: Order
1.5: Outline of This Book
Exercises

Chapter 2 – Divide-and-Conquer
Overview
2.1: Binary Search
2.2: Mergesort
2.3: The Divide-and-Conquer Approach
2.4: Quicksort (Partition Exchange Sort)
2.5: Strassen’s Matrix Multiplication Algorithm
2.6: Arithmetic with Large Integers
2.7: Determining Thresholds
2.8: When Not to Use Divide-and-Conquer
Exercises

Chapter 3 – Dynamic Programming
Overview
3.1: The Binomial Coefficient
3.2: Floyd’s Algorithm for Shortest Paths
3.3: Dynamic Programming and Optimization Problems
3.4: Chained Matrix Multiplication
3.5: Optimal Binary Search Trees
3.6: The Traveling Salesperson Problem
3.7: Sequence Alignment
Exercises

Chapter 4 – The Greedy Approach
Overview
4.1: Minimum Spanning Trees
4.2: Dijkstra’s Algorithm for Single-Source Shortest Paths
4.3: Scheduling
4.4: Huffman Code
4.5: The Greedy Approach versus Dynamic Programming: The Knapsack Problem
Exercises

Chapter 5 – Backtracking
Overview
5.1: The Backtracking Technique
5.2: The n-Queens Problem
5.3: Using a Monte Carlo Algorithm to Estimate the Efficiency of a Backtracking Algorithm
5.4: The Sum-of-Subsets Problem
5.5: Graph Coloring
5.6: The Hamiltonian Circuits Problem
5.7: The 0–1 Knapsack Problem
Exercises

Chapter 6 – Branch-and-Bound
Overview
6.1: Illustrating Branch-and-Bound with the 0–1 Knapsack problem
6.2: The Traveling Salesperson Problem
6.3: Abductive Inference (Diagnosis)
Exercises

Chapter 7 – Introduction to Computational Complexity: The Sorting Problem
7.1: Computational Complexity
7.2: Insertion Sort and Selection Sort
7.3: Lower Bounds for Algorithms that Remove at Most One Inversion Per Comparison
7.4: Mergesort Revisited
7.5: Quicksort Revisited
7.6: Heapsort
7.7: Comparison of Mergesort, Quicksort, and Heapsort
7.8: Lower Bounds for Sorting Only by Comparison of Keys
7.9: Sorting by Distribution (Radix Sort)
Exercises




Chapter 8 – More Computational Complexity: The Searching Problem
Overview
8.1: Lower Bounds for Searching Only by Comparisons of Keys
8.2: Interpolation Search
8.3: Searching in Trees
8.4: Hashing
8.5: The Selection Problem: Introduction to Adversary Arguments
Exercises

Chapter 9 – Computational Complexity and Interactability: An Introduction to the Theory of NP
Overview
9.1: Interactability
9.2: Input Size Revisited
9.3: The Three General Problem Categories
9.4: The Theory of NP
9.5: Handling NP-Hard Problems
Exercises

Chapter 10 – Number-Theoretic Algorithms
Overview
10.1: Number Theory Review
10.2: Computing the Greatest Common Divisor
10.3: Modular Arithmetic Review
10.4: Solving Modular Linear Equations
10.5: Computing Modular Powers
10.6: Finding Large Prime Numbers
10.7: The RSA Public-Key Cryptosystem
Exercises

Chapter 11 – Introduction to Parallel Algorithms
Overview
11.1: Parallel Architectures
11.2: The PRAM Model
Exercises

Appendix A – Review of Necessary Mathematics
A.1: Notation
A.2: Functions
A.3: Mathematical Induction
A.4: Theorems and Lemmas
A.5: Logarithms
A.6: Sets
A.7: Permutations and Combinations
A.8: Probability
Exercises

Appendix B – Solving Recurrence Equations: With Applications to Analysis of Recursive Algorithms
B.1: Solving Recurrences Using Induction
B.2: Solving Recurrences Using the Characteristic Equation
B.3: Solving Recurrences by Substitution
B.4: Extending Results for n, a Power of a Positive Constant b, to n in General
B.5: Proofs of Theorems
Exercises

Appendix C – Data Structures for Disjoint Sets
References

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