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Design and Analysis of Algorithms - CS6402

Design and Analysis of Algorithms






Introduction to The Design and Analysis of Algorithms by Anany Levitin

Chapter 1 Introduction

-:- Introduction to the Design and Analysis of Algorithms
-:- What Is an Algorithm?
-:- Fundamentals of Algorithmic Problem Solving
-:- Ascertaining the Capabilities of the Computational Device
-:- 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
-:- Important Problem Types in Algorithms Analysis
-:- Fundamental Data Structures

Chapter 2 Fundamentals of the Analysis of Algorithm Eficiency

-:- The Analysis Framework
-:- Asymptotic Notations and Basic Efficiency Classes
-:- Mathematical Analysis of Non recursive Algorithms
-:- Mathematical Analysis of Recursive Algorithms
-:- Example: Computing the nth Fibonacci Number
-:- Empirical Analysis of Algorithms
-:- Algorithm Visualization

Chapter 3 Brute Force and Exhaustive Search

-:- Brute Force and Exhaustive Search
-:- Selection Sort and Bubble Sort
-:- Sequential Search and Brute-Force String Matching
-:- Closest-Pair and Convex-Hull Problems by Brute Force
-:- Exhaustive Search
-:- Depth-First Search and Breadth-First Search

Chapter 4 Decrease and Conquer

-:- Decrease and Conquer
-:- Insertion Sort
-:- Topological Sorting
-:- Algorithms for Generating Combinatorial Objects
-:- Decrease by a Constant Factor Algorithms
-:- Variable Size Decrease Algorithms

Chapter 5 Divide and Conquer

-:- Divide and Conquer
-:- Mergesort
-:- Quicksort
-:- Binary Tree Traversals and Related Properties
-:- Multiplication of Large Integers
-:- Strassen’s Matrix Multiplication
-:- The Closest Pair Problem by Divide and Conquer
-:- Convex Hull Problems by Divide and Conquer

Chapter 6 Transform and Conquer

-:- Transform and Conquer
-:- Presorting
-:- Gaussian Elimination
-:- Balanced Search Trees: AVL Trees and 2-3 Trees
-:- Heaps and Heapsort
-:- Horner’s Rule and Binary Exponentiation
-:- Problem Reduction

Chapter 7 Space and Time Trade Offs

-:- Space and Time Trade-Offs
-:- Sorting by Counting
-:- Input Enhancement in String Matching: Horspool’s and Boyer-Moore Algorithm
-:- Open and Closed Hashing
-:- B-Trees Algorithms

Chapter 8 Dynamic Programming

-:- Dynamic Programming
-:- Dynamic Programming: Three Basic Examples
-:- The Knapsack Problem and Memory Functions
-:- Optimal Binary Search Trees
-:- Warshall’s and Floyd’s Algorithms

Chapter 9 Greedy Technique

-:- Greedy Technique
-:- Prim’s Algorithm
-:- Kruskal’s Algorithm
-:- Dijkstra’s Algorithm
-:- Huffman Trees and Codes

Chapter 10 Iterative Improvement

-:- Iterative Improvement
-:- The Simplex Method
-:- The Iterative Maximum-Flow Problem
-:- Maximum Matching in Bipartite Graphs
-:- The Stable Marriage Problem

Chapter 11 Limitations of Algorithm Power

-:- Limitations of Algorithm Power
-:- Lower-Bound Arguments
-:- Decision Trees algorithms
-:- P , NP , and NP-Complete Problems
-:- Challenges of Numerical Algorithms

Chapter 12 Coping with the Limitations of Algorithm Power

-:- Coping with the Limitations of Algorithm Power
-:- Backtracking
-:- Branch-and-Bound
-:- Approximation Algorithms for NP -Hard Problems
-:- Approximation Algorithms for the Traveling Salesman Problem
-:- Approximation Algorithms for the Knapsack Problem
-:- Algorithms for Solving Nonlinear Equations