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The course is one of the courses of Master of Computer Applications programme of IGNOU. Algorithms are the central part of computing and Design and Analysis of algorithms course is the core of the study of Computer Science discipline. This course helps you design and analyse algorithms. The topics included in the course are: 1. Introduction to Algorithms Basics of an Algorithm and its properties: Basics building blocks of Algorithms, A survey of common running time, Analysis & Complexity of Algorithm. Some pre-requisites and Asymptotic Bounds: Some Useful Mathematical Functions & Notations (Functions &Notations, Modular Arithmetic/Mod Function, Mathematical Expectation, Principle of Mathematical Induction). Analysis of Simple Algorithm: Complexity analysis of Algorithms, Euclid Algorithm for GCD, Polynomial Evaluation Algorithm, Exponent Evaluation, Sorting Algorithm Solving Recurrences: Substitution Methods, Iteration Methods, Recursive Tree Methods, Master Methods 2. Design Techniques-I Greedy Technique, Some Examples to understand Greedy Techniques, Formalization of Greedy Techniques, An overview of local and global optima, Fractional Knapsack problem, Huffman Codes, A task scheduling algorithm Divide & Conquer Technique: General Issues in Divide and Conquer Technique, Binary Search Algorithm, Sorting Algorithm (Merge Sort Quick Sort), Matrix Multiplication Algorithm Graph Algorithm –I: Basic Definition and terminologies, Graph Representation (Adjacency Matrix, Adjacency List), (Graph Traversal Algorithms (Depth First Search, Breadth First Search), Topological Sort, Strongly Connected Components) 3. Design Techniques – II Graph Algorithms- II: Minimum Cost Spanning Tree problems, (Kruskal’s Algorithm, Prim’s Algorithm), Single Source Shortest Path Problems (Bellman Ford Algorithm, Dijkstra’s Algorithm), Maximum Bipartite Matching Problem Dynamic Programming Technique: The Principle of Optimality, Chained Matrix Multiplication, Matrix Multiplication Using Dynamic Programming, Optimal binary search trees problems, Binomial coefficient computation, Floyd Warshall algorithm String Matching Techniques: The naïve String-Matching Algorithm, The Rabin Karp Algorithm, Knuth –Morris Pratt Algorithm 4. NP-Completeness and Approximation Algorithm NP-Completeness: Concepts of Class-P, NP-Completeness, NP-Hard, Unsolvable problems, Polynomial-time, Polynomial-time Reductions, Class P with Examples, Knapsack and TSP problems NP-Completeness and NP-Hard Problems: Polynomial Time verification, Techniques to show NP- Hardness, NP-Complete problems and P Vs NP problems? Handling Intractability: Approximation algorithms for Vertex Cover problem and minimizing make span as parallel machines (Graham’s algorithm), Parameterized algorithm for Vertex Cover problem, Meta-heuristic Algorithms
