FPTAS for Knapsack

This lecture covers the Fully Polynomial-Time Approximation Scheme (FPTAS) for the Knapsack problem, presenting algorithms and proofs for achieving an approximation of (1-ε) times the optimal solution. The instructor explains the dynamic programming approach, pseudo-polynomial time complexity, and the process of solving the Knapsack problem efficiently. Various approximation algorithms are discussed, along with their running times and theoretical proofs. The lecture concludes with the analysis of profit maximization and the relationship between the obtained solution and the optimal solution.