区间不确定性模型下鲁棒近似算法的可复用框架
A Reusable Framework for Robust Approximation Algorithms in the Interval Uncertainty Model
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中文总结 AI 辅助
本文推广了区间不确定性下鲁棒优化的框架，提出将局部搜索近似算法转化为鲁棒近似算法的定理，并首次给出加权k-集合覆盖的鲁棒近似算法。
中文摘要 AI 辅助
区间不确定性下的鲁棒优化旨在计算在由区间约束成本描述的一系列场景中表现良好的解决方案。本文重新审视了Ganesh、Maggs和Panigrahi于2020年提出的框架，该框架用于研究NP难问题在区间不确定性下的鲁棒优化。我们首先推广了$\ell=0$情形下的一个结果，该结果将一类近似算法转化为鲁棒近似算法。此外，在一般情形下，我们提供了一个定理，该定理在局部搜索算法的移动满足三个新形式化条件时，可将任何基于局部搜索的近似算法转化为鲁棒近似算法。我们随后利用该结果提出了加权$k$-集合覆盖问题的首个鲁棒近似算法，这是继Ganesh、Maggs和Panigrahi论文发表后已知的第三个承认鲁棒近似的NP难问题，也是首个此类算法。
英文摘要
Robust optimization under interval uncertainty aims to compute solutions that perform well on a range of scenarios that are described by interval-constrained costs. In this paper, we revisit a framework introduced by Ganesh, Maggs and Panigrahi in 2020 to study the robust optimization of NP-hard problems under interval uncertainty. We start by generalizing a result in the $\ell=0$ case, which transforms a category of approximation algorithms into a robust approximation algorithm. Furthermore, in the general case, we provide a theorem that turns any local search-based approximation algorithm into a robust approximation algorithm under three newly formalized conditions over the moves of the local search algorithm. We then use this result to present the first robust approximation algorithm for Weighted $k$-Set Cover, the third NP-hard problem known to admit a robust approximation, and the first since the publication of Ganesh, Maggs and Panigrahi's paper.
发表机构
- CNRS, LaBRI, University of Bordeaux（法国国家科学研究中心，LaBRI，波尔多大学）
- University of Augsburg（奥格斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。
