About Lecture - 1 Overview of the course

NP-Completeness of Minimax Job Scheduling via Matching Reductions Greedy Approximation Algorithms for Set Cover and K-Center Problems Approximation Algorithms for NP-Complete Problems: Metric TSP and Precedence Scheduling Fully Polynomial Time Approximation Scheme (FPTAS) for the Knapsack Problem NP-Completeness of Bounded-Degree Vertex Cover and Exact Cover via Reduction Average Case Analysis of Quicksort Time and Space Complexity Analysis of Algorithms Divide and Conquer Recurrence Analysis: Merge Sort, Quicksort Partitioning, and Median Selection Proving Greedy Algorithm Correctness via Induction and Exchange Arguments Branch and Bound: Pruning via Admissible Cost Function Bounds Random Access Machine Model for Algorithm Time Complexity Analysis Knuth-Morris-Pratt Pattern Matching via the Prefix Function Element Distinctness Lower Bounds in Decision Tree Model Longest Common Subsequence via Dynamic Programming Deterministic Linear-Time Median Finding via Median-of-Medians Ω(n log n) Lower Bound for Comparison-Based Sorting via Decision Trees NP-Completeness Reductions Among Clique, Independent Set, and Vertex Cover Greedy Algorithms: Fractional Knapsack and Huffman Coding Sorting Lower Bounds via Comparison Decision Trees Finding Minimum and Second Minimum in Arrays Using Divide and Conquer Bipartite Maximum Matching via Augmenting Paths (Berge Theorem) Matrix Chain Multiplication Optimization via Dynamic Programming Dynamic Programming for Production Scheduling with Startup and Holding Costs Greedy Algorithms: Maximum Independent Set on Trees and Interval Scheduling KMP Algorithm: Computing the Pattern Matching Failure Function Reductions Between Hamiltonian Cycle and Hamiltonian Path Problems Backtrack Search for Combinatorial Optimization Problems Closest Pair Problem in Computational Geometry via Divide and Conquer Knapsack Problem Optimization Using Dynamic Programming NP Completeness: Verifier-Prover Certificates and Cook's Theorem Huffman Coding Optimality Proof via the Exchange Argument Asymptotic Notation in Algorithm Analysis NP-Completeness Proof via Subset Sum and Exact Cover Reductions