Design and Analysis of Algorithms(DAA) Syllabus

Course Description: This course introduces basic elements of the design and analysis of computer algorithms. Topics include asymptotic notations and analysis, divide and conquer strategy, greedy methods, dynamic programming, basic graph algorithms, NP-completeness, and approximation algorithms. For each topic, beside in-depth coverage, one or more representative problems and their algorithms shall be discussed. Course Objectives: 

•    Analyze the asymptotic performance of algorithms.
•    Demonstrate a familiarity with major algorithm design techniques 
•    Apply important algorithmic design paradigms and methods of analysis. 
•    Solve simple to moderately difficult algorithmic problems arising in applications.
•    Able to demonstrate the hardness of simple NP-complete problems

1. Foundation of Algorithm Analysis

teaching hours: 4 hrs

1.1. Algorithm and its properties, RAM model, Time and Space Complexity, detailed analysis

of algorithms (Like factorial algorithm), Concept of Aggregate Analysis

1.2. Asymptotic Notations: Big-O, Big-Ω and Big-Ө Notations their Geometrical Interpretation

and Examples.

1.3. Recurrences: Recursive Algorithms and Recurrence Relations, Solving Recurrences

(Recursion Tree Method, Substitution Method, Application of Masters Theorem)

2. Iterative Algorithms

teaching hours: 4 hrs

2.1. Basic Algorithms: Algorithm for GCD, Fibonacci Number and analysis of their time and

space complexity

2.2. Searching Algorithms: Sequential Search and its analysis

2.3. Sorting Algorithms: Bubble, Selection, and Insertion Sort and their Analysis

3. Divide and Conquer Algorithms

teaching hours: 8 hrs

3.1. Searching Algorithms: Binary Search, Min-Max Finding and their Analysis

3.2. Sorting Algorithms: Merge Sort and Analysis, Quick Sort and Analysis (Best Case, Worst

Case and Average Case), Heap Sort (Heapify, Build Heap and Heap Sort Algorithms and

their Analysis), Randomized Quick sort and its Analysis

3.3. Order Statistics: Selection in Expected Linear Time, Selection in Worst Case Linear Time

and their Analysis.

4. Greedy Algorithms

teaching hours: 6 hrs

4.1. Optimization Problems and Optimal Solution, Introduction of Greedy Algorithms,

Elements of Greedy Strategy.

4.2. Greedy Algorithms: Fractional Knapsack, Job sequencing with Deadlines, Kruskal’s

Algorithm, Prims Algorithm, Dijkstra’s Algorithm and their Analysis

4.3. Huffman Coding: Purpose of Huffman Coding, Prefix Codes, Huffman Coding

Algorithm and its Analysis

5. Dynamic Programming

teaching hours: 8 hrs

5.1. Greedy Algorithms vs Dynamic Programming, Recursion vs Dynamic Programming,

Elements of DP Strategy

5.2. DP Algorithms: Matrix Chain Multiplication, String Editing, Zero-One Knapsack

Problem, Floyd Warshwall Algorithm, Travelling Salesman Problem and their

Analysis.

5.3. Memoization Strategy, Dynamic Programming vs Memoization

6. Backtracking

teaching hours: 5 hrs

6.1. Concept of Backtracking, Recursion vs Backtracking

6.2. Backtracking Algorithms: Subset-sum Problem, Zero-one Knapsack Problem, N-queen

Problem and their Analysis.

7. Number Theoretic Algorithms

teaching hours: 5 hrs

7.1. Number Theoretic Notations, Euclid’s and Extended Euclid’s Algorithms and their

Analysis.

7.2. Solving Modular Linear Equations, Chinese Remainder Theorem, Primility Testing: Miller-

Rabin Randomized Primility Test and their Analysis

8. NP Completeness

teaching hours: 5 hrs

8.1. Tractable and Intractable Problems, Concept of Polynomial Time and Super Polynomial

Time Complexity

8.2. Complexity Classes: P, NP, NP-Hard and NP-Complete

8.3. NP Complete Problems, NP Completeness and Reducibility, Cooks Theorem, Proofs of NP

Completeness (CNF-SAT, Vertex Cover and Subset Sum)

8.4. Approximation Algorithms: Concept, Vertex Cover Problem, Subset Sum Problem

Laboratory Works:

This course can be learnt in effective way only if we give focus is given in practical

aspects of algorithms and techniques discussed in class. Therefore student should be able

to implement the algorithms and analyze their behavior.

For the laboratory work, students should implement the following algorithms in C/ C++

and perform their analysis for time and space complexity.

1. Basic iterative algorithms GCD algorithm, Fibonacci Sequences, Sequential and Binary

Search.

2. Basic iterative sorting algorithms: Bubble Sort, selection Sort, Insertion Sort.

3. Binary Search with Divide and conquer approach.

4. Merge Sort, Heap sort, Quick Sort, Randomized Quick Sort.

5. Selection Problem with divide and Conquer approach

6. Fractional Knapsack Problem, Job sequencing with deadline, Kruskal’s algorithm, Prims

algorithm, Dijkstra’s Algorithm

7. Implement the dynamic programming algorithms.

8. Algorithms using Backtracking approach.

9. Implement approximation Algorithm.