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October 1, 2025Open Access

Weakly Approximating Knapsack in Subquadratic Time

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An algorithm was developed that solves knapsack in approximately O(n + (1/ε)^{7/4}) time.
The method achieves results for total profit at least OPT/(1+ε) with total weight at most (1 + ε)t.
This approach challenges previous assumptions regarding the limits of subquadratic time solutions.
The findings suggest potential advancements in solving classic optimization problems like knapsack.

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The study demonstrates an algorithm solving knapsack with optimal value in subquadratic time, suggesting new bounds for total profit.

Chen et al. (2025) studied this question.

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