Module 1: Introduction to Data Structures
- Overview of Data Structures
- Types of Data Structures
- Arrays and Linked Lists
- Stacks and Queues
- Trees and Graphs
- Hash Tables
- Heaps
- Priority Queues
- Searching Algorithms
- Sorting Algorithms
- Big O Notation
- Memory Management
- Recursion
- Dynamic Programming
Module 2: Algorithmic Design Techniques
- Greedy Algorithms
- Divide and Conquer Algorithms
- Dynamic Programming
- Backtracking Algorithms
- Branch and Bound Algorithms
- Network Flow Algorithms
- Linear Programming
- Approximation Algorithms
- Randomized Algorithms
- Heuristic Algorithms
Module 3: Dynamic Programming
- Introduction to Dynamic Programming
- Applications of Dynamic Programming
- Greedy Algorithms vs Dynamic Programming
- Memoization and Tabulation
- Longest Common Subsequence
- Optimal Substructure and Overlapping Subproblems
- 0-1 Knapsack Problem
- Matrix Chain Multiplication
- Bellman-Ford Algorithm
- Floyd-Warshall Algorithm
Module 4: Greedy Algorithms
- Introduction to Greedy Algorithms
- Greedy Algorithms for Optimization Problems
- Greedy Algorithms for Graph Problems
- Greedy Algorithms for Scheduling Problems
- Greedy Algorithms for Knapsack Problems
- Greedy Algorithms for Sorting Problems
- Greedy Algorithms for String Matching Problems
- Greedy Algorithms for Network Flow Problems
- Greedy Algorithms for Approximation Algorithms
- Greedy Algorithms for NP-Hard Problems
Module 5: Graph Algorithms
- Introduction to Graph Algorithms
- Breadth-First Search Algorithm
- Depth-First Search Algorithm
- Shortest Path Algorithms
- Minimum Spanning Tree Algorithms
- Network Flow Algorithms
- Maximum Flow Algorithms
- Connectivity Algorithms
- Matching Algorithms
- Eulerian Path Algorithms
- Hamiltonian Path Algorithms
- Graph Coloring Algorithms
- Topological Sorting Algorithms
- Graph Isomorphism Algorithms
- Graph Partitioning Algorithms
- Graph Drawing Algorithms
- Graph Clustering Algorithms
- Graph Optimization Algorithms
- Graph Search Algorithms
- Graph Traversal Algorithms
Module 6: Network Flow Algorithms
- Introduction to Network Flow Algorithms
- Maximum Flow Problem
- Minimum Cost Flow Problem
- Ford-Fulkerson Algorithm
- Edmonds-Karp Algorithm
- Dinic's Algorithm
- Push-Relabel Algorithm
- Goldberg-Tarjan Algorithm
- Network Simplex Algorithm
- Applications of Network Flow Algorithms
Module 7: Linear Programming
- Introduction to Linear Programming
- Formulating Linear Programming Problems
- Graphical Solution of Linear Programming Problems
- Simplex Method for Solving Linear Programming Problems
- Duality in Linear Programming
- Sensitivity Analysis in Linear Programming
- Integer Programming
- Transportation and Assignment Problems
- Network Flow Problems
- Project Scheduling Problems
Module 8: Integer Programming
- Introduction to Integer Programming
- Formulating Integer Programming Problems
- Linear Programming Relaxations
- Branch and Bound Algorithms
- Cutting Plane Algorithms
- Column Generation Algorithms
- Integer Programming Applications
- Advanced Integer Programming Techniques
- Integer Programming Software
- Integer Programming Modeling Examples
Module 9: Approximation Algorithms
- Introduction to Approximation Algorithms
- Greedy Algorithms
- Randomized Algorithms
- Local Search Algorithms
- Linear Programming Relaxation
- Primal-Dual Algorithms
- Semidefinite Programming Relaxation
- Approximation Algorithms for NP-Hard Problems
- Approximation Algorithms for Graph Problems
- Approximation Algorithms for Combinatorial Optimization Problems
- Approximation Algorithms for Machine Learning Problems
- Approximation Algorithms for Data Mining Problems
- Approximation Algorithms for Image Processing Problems
- Approximation Algorithms for Network Design Problems
- Approximation Algorithms for Scheduling Problems
- Approximation Algorithms for Online Problems
- Approximation Algorithms for Distributed Systems
- Approximation Algorithms for Big Data Problems
- Approximation Algorithms for Cloud Computing
- Approximation Algorithms for Internet of Things (IoT)
Module 10: NP-Completeness
- Introduction to NP-Completeness
- Polynomial Time Reductions
- Cook-Levin Theorem
- Verifying NP-Completeness
- NP-Complete Problems
- Approximation Algorithms
- NP-Hard Problems
- Coping with NP-Completeness
- NP-Completeness in Practice
- Advanced Topics in NP-Completeness
Module 11: Parallel Algorithms
- Introduction to Parallel Algorithms
- Designing Parallel Algorithms
- Parallel Algorithms for Sorting and Searching
- Parallel Algorithms for Graphs
- Parallel Algorithms for Matrix Operations
- Parallel Algorithms for Numerical Computations
- Parallel Algorithms for Image Processing
- Parallel Algorithms for Data Mining
- Parallel Algorithms for Machine Learning
- Parallel Algorithms for Natural Language Processing
- Parallel Algorithms for Big Data Analysis
- Parallel Algorithms for Cloud Computing
- Parallel Algorithms for High Performance Computing
- Parallel Algorithms for Distributed Systems
- Parallel Algorithms for Embedded Systems
Module 12: Advanced Topics in Dynamic Programming
- Reinforcement Learning and Dynamic Programming
- Multi-Objective Dynamic Programming
- Stochastic Dynamic Programming
- Approximate Dynamic Programming
- Optimal Control Theory
- Markov Decision Processes
- Dynamic Programming for Optimal Control
- Dynamic Programming for Markov Decision Processes
- Dynamic Programming for Multi-Agent Systems
- Dynamic Programming for Robotics
- Dynamic Programming for Resource Allocation
- Dynamic Programming for Network Optimization
- Dynamic Programming for Game Theory
- Dynamic Programming for Machine Learning
- Dynamic Programming for Optimization Problems