We study the edge-weighted online stochastic matching problem. Since Feldman, Mehta, Mirrokni, and Muthukrishnan proposed the $(1-\frac1e)$-competitive Suggested Matching algorithm, there has been no improvement for the general edge-weighted online stochastic matching problem. In this paper, we introduce the first algorithm beating the $1-\frac1e$ barrier in this setting, achieving a competitive ratio of $0.645$. Under the LP proposed by Jaillet and Lu, we design an algorithmic preprocessing, dividing all edges into two classes. Then based on the Suggested Matching algorithm, we adjust the matching strategy to improve the performance on one class in the early stage and on another class in the late stage, while keeping the matching events of different edges highly independent. By balancing them, we finally guarantee the matched probability of every single edge.

翻译：我们研究边加权在线随机匹配问题。自Feldman、Mehta、Mirrokni和Muthukrishnan提出$(1-\frac1e)$竞争比的建议匹配算法以来，一般性边加权在线随机匹配问题尚未取得任何改进。本文首次引入突破该环境下$1-\frac1e$壁垒的算法，实现了$0.645$的竞争比。基于Jaillet和Lu提出的线性规划，我们设计了一种算法预处理方法，将所有边分为两类。随后在建议匹配算法的基础上调整匹配策略，在早期阶段改进对第一类边的性能，在后期阶段改进对第二类边的性能，同时保持不同边的匹配事件高度独立。通过平衡两者，我们最终保证了每条边的匹配概率。