A simple $(2+ε)$-approximation for knapsack interdiction
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915952338141184 |
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| author | Weninger, Noah |
| author_facet | Weninger, Noah |
| contents | In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict (delete) subject to the budget which minimizes the maximum profit attainable by packing the remaining items subject to the capacity. We present a $(2+ε)$-approximation running in $O(n^3ε^{-1}\log(ε^{-1}\log\sum_i p_i))$ time. Although a polynomial-time approximation scheme (PTAS) is already known for this problem, our algorithm is considerably simpler and faster. The approach also generalizes naturally to a $(1+t+ε)$-approximation for $t$-dimensional knapsack interdiction with running time $O(n^{t+2}ε^{-1}\log(ε^{-1}\log\sum_i p_i))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A simple $(2+ε)$-approximation for knapsack interdiction Weninger, Noah Data Structures and Algorithms In the knapsack interdiction problem, there are $n$ items, each with a non-negative profit, interdiction cost, and packing weight. There is also an interdiction budget and a capacity. The objective is to select a set of items to interdict (delete) subject to the budget which minimizes the maximum profit attainable by packing the remaining items subject to the capacity. We present a $(2+ε)$-approximation running in $O(n^3ε^{-1}\log(ε^{-1}\log\sum_i p_i))$ time. Although a polynomial-time approximation scheme (PTAS) is already known for this problem, our algorithm is considerably simpler and faster. The approach also generalizes naturally to a $(1+t+ε)$-approximation for $t$-dimensional knapsack interdiction with running time $O(n^{t+2}ε^{-1}\log(ε^{-1}\log\sum_i p_i))$. |
| title | A simple $(2+ε)$-approximation for knapsack interdiction |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2604.21877 |