We investigate non-adaptive algorithms for matroid prophet inequalities. Matroid prophet inequalities have been considered resolved since 2012 when [KW12] introduced thresholds that guarantee a tight 2-approximation to the prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and [FSZ16] have used non-adaptive thresholds with a feasibility restriction; however, this translates to adaptively changing an item's threshold to infinity when it cannot be taken with respect to the additional feasibility constraint, hence the algorithm is not truly non-adaptive. A major application of prophet inequalities is in auction design, where non-adaptive prices possess a significant advantage: they convert to order-oblivious posted pricings, and are essential for translating a prophet inequality into a truthful mechanism for multi-dimensional buyers. The existing matroid prophet inequalities do not suffice for this application. We present the first non-adaptive constant-factor prophet inequality for graphic matroids.

中文翻译：

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非自适应拟阵先知不等式

我们研究拟阵先知不等式的非自适应算法。自 2012 年 [KW12] 引入保证严格 2 近似于先知的阈值以来，拟阵先知不等式被认为已得到解决；然而，这个算法是自适应的。[CHMS10] 和 [FSZ16] 的其他方法使用了具有可行性限制的非自适应阈值；然而，这转化为在不能考虑额外的可行性约束时自适应地将项目的阈值更改为无穷大，因此该算法并不是真正的非自适应。先知不等式的一个主要应用是在拍卖设计中，其中非自适应价格具有显着优势：它们转换为订单无意识的发布定价，并且对于将先知不平等转化为多维买家的真实机制至关重要。现有拟阵先知不等式不足以满足此应用程序的要求。我们提出了图形拟阵的第一个非自适应常数因子先知不等式。