非强制检查的潘多拉盒子问题：困难性与近似方案
Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme
摘要：
Weitzman（1979）引入了潘多拉盒子问题作为有检查成本的顺序搜索模型，并给出了一个优雅的基于索引的策略，可以获得可证明的最优预期收益。在各种场景中，搜索代理可以选择选项而不进行昂贵的检查。非强制性检查的潘多拉盒子问题的变体引起了经济学和算法研究人员的兴趣。各种简单的算法已被证明是次优的，其中最著名的是Guha等人（2008年）提出的0.8-近似算法。该问题的硬度结果未知。在这项工作中，我们表明，这是NP-难计算的最优政策潘多拉的问题，非强制性检查。我们还给出了一个多项式时间近似方案（PTAS），计算的预期回报至少$(1 - ε)$ -分数的最佳政策，为任意小的$ε> 0$。另一方面，我们证明了问题的决策版本是NP的。
英文摘要：
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In various scenarios, the searching agent may select an option without making a costly inspection. The variant of the Pandora box problem with non-obligatory inspection has attracted interest from both economics and algorithms researchers. Various simple algorithms have proved suboptimal, with the best known 0.8-approximation algorithm due to Guha et al. (2008). No hardness result for the problem was known. In this work, we show that it is NP-hard to compute an optimal policy for Pandora's problem with nonobligatory inspection. We also give a polynomial-time approximation scheme (PTAS) that computes policies with an expected payoff at least $(1 - ε)$-fraction of the optimal, for arbitrarily small $ε> 0$. On the side, we show the decision version of the problem to be in NP.
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