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arXiv · 2512.21195

An O(nlogn) approximate knapsack algorithm

Nick Dawes
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Abstract

A modified dynamic programming algorithm rapidly and accurately solves large 0/1 knapsack problems. It has computational O(nlogn), space O(nlogn) and predictable maximum error. Experimentally it's accuracy increases faster than linearly with the solution size k. Problems with k=1e3 are solved with an average maximum fractional error of 1e-4 and problems with k=1e5 with an average maximum fractional error of 1e-7. The algorithm runs in constant time for all problems with a given n. On a common desktop computer the algorithm processes n=1e3 problems in 1e-3 seconds and n=1e6 problems in 2 seconds.

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Nick Dawes. 2025-12-24. An O(nlogn) approximate knapsack algorithm. https://arxiv.org/abs/2512.21195

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