Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching models. Here, each edge in the graph has a known, independent probability of existing derived from some prediction. Algorithms must probe edges to determine existence and match them irrevocably if they exist. Further, each vertex may have a patience constraint denoting how many of its neighboring edges can be probed. We present new ordered contention resolution schemes yielding improved approximation guarantees for some of the foundational problems studied in this area. For stochastic matching with patience constraints in general graphs, we provide a 0.382-approximate algorithm, significantly improving over the previous best 0.31-approximation of Baveja et al. (2018). When the vertices do not have patience constraints, we describe a 0.432-approximate random order probing algorithm with several corollaries such as an improved guarantee for the Prophet Secretary problem under Edge Arrivals. Finally, for the special case of bipartite graphs with unit patience constraints on one of the partitions, we show a 0.632-approximate algorithm that improves on the recent $1/3$-guarantee of Hikima et al. (2021).

翻译：匹配是许多领域最根本和广泛应用的问题之一。 在这些不同的现实应用中, 输入中往往存在一定程度的不确定性, 从而导致对随机匹配模型的研究。 这里, 图表中的每个边缘都有从某些预测中得出的已知、 独立的现有概率。 算法必须探索边缘, 以确定存在与否, 如果存在的话, 不可撤销地匹配。 此外, 每个顶端可能有一个耐性约束, 说明有多少相邻边缘可以被探测。 我们提出了新的有秩序的争议解决方案, 使该领域研究的一些基本问题得到更好的近似保障。 对于与一般图表中的耐力制约相匹配的随机匹配, 我们提供0. 382 近似方算法, 大大改进了先前最佳的巴维贾等人( 2018年) 0. 0. 31 的适应性。 当脊椎没有耐性约束时, 我们描述一种0. 432 近似随机随机排序算法, 包括改善对伊杰· 阿里瓦尔所研究的一些基本问题的预秘书问题的保证。 最后, 我们提供一种与一般图表中的耐受力 。 0. 0. 0. 0. 0. 0. 3 图表 显示我们 16 的压 的 的 度 的 的 的 的 度 度 的 的 的 。