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Fully Polynomial-Time Approximation Scheme for the Knapsack Problem
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We first present a pseudo-polynomial time algorithm for the knapsack problem, which we then use as a basis for a fully polynomial-time approximation scheme. There is also some complexity theory in this video, since we need concepts like pseudo-polynomial (vs. polynomial) time algorithms, weakly (vs. strongly) NP-hard problems, and of course (fully) polynomial time approximation schemes.
00:00 Knapsack problem
03:47 pseudo-polynomial algorithms
06:34 strongly vs weakly NP-hard
07:44 pseudo-polynomial algorithm for Knapsack
12:29 Recurrence for the DP
16:06 Executing the DP
19:44 (Fully) Polynomial-Time Approximation Schemes
22:18 FPTAS for Knapsack
24:45 Analysis
29:11 Strong NP-hard vs FPTAS
00:00 Knapsack problem
03:47 pseudo-polynomial algorithms
06:34 strongly vs weakly NP-hard
07:44 pseudo-polynomial algorithm for Knapsack
12:29 Recurrence for the DP
16:06 Executing the DP
19:44 (Fully) Polynomial-Time Approximation Schemes
22:18 FPTAS for Knapsack
24:45 Analysis
29:11 Strong NP-hard vs FPTAS
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