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  "path": "/abs/2604.21877v1",
  "publishedAt": "2026-04-24T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Noah Weninger"
  ],
  "textContent": "**Authors:** Noah Weninger\n\nIn 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"
}