0-1背包的近似格式

Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA) Pub Date : 2018-01-01 DOI:10.4230/OASIcs.SOSA.2018.5

Timothy M. Chan

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引用次数: 40

摘要

我们重新审视标准的0-1背包问题。最新的由Rhee(2015)提出的近似因子为1+eps的多项式时间近似方案，其运行时间接近O(n+(1/eps)^{5/2})(忽略多对数因子)，并且是随机化的。我们提出了一种更简单的算法，可以达到相同的结果，并且是确定性的。通过更多的努力，我们的想法实际上可以在O(n + (1/eps)^{12/5})附近得到改进的时间限制，并且对于较小的n还可以进一步改进。

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Approximation Schemes for 0-1 Knapsack

We revisit the standard 0-1 knapsack problem. The latest polynomial-time approximation scheme by Rhee (2015) with approximation factor 1+eps has running time near O(n+(1/eps)^{5/2}) (ignoring polylogarithmic factors), and is randomized. We present a simpler algorithm which achieves the same result and is deterministic. With more effort, our ideas can actually lead to an improved time bound near O(n + (1/eps)^{12/5}), and still further improvements for small n.

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Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)

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