A Nearly Quadratic-Time FPTAS for Knapsack

08/15/2023

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by   Lin Chen, et al.

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We investigate polynomial-time approximation schemes for the classic 0-1 knapsack problem. The previous algorithm by Deng, Jin, and Mao (SODA'23) has approximation factor 1 + with running time O(n + 1/^2.2). There is a lower Bound of (n + 1/)^2-o(1) conditioned on the hypothesis that (min, +) has no truly subquadratic algorithm. We close the gap by proposing an approximation scheme that runs in O(n + 1/^2) time.