In the stochastic weighted matching problem, the goal is to find a large-weight matching of a graph when we are uncertain about the existence of its edges. In particular, each edge $e$ has a known weight $w_e$ but is realized independently with some probability $p_e$. The algorithm may query an edge to see whether it is realized. We consider the well-studied query commit version of the problem, in which any queried edge that happens to be realized must be included in the solution. Gamlath, Kale, and Svensson showed that when the input graph is bipartite, the problem admits a $(1-1/e)$-approximation. In this paper, we give an algorithm that for an absolute constant $\delta > 0.0014$ obtains a $(1-1/e+\delta)$-approximation, therefore breaking this prevalent bound.

翻译：在随机加权匹配问题中,目标是当我们不确定其边缘是否存在时,找到一个图表的重量匹配。 特别是, 每个边缘美元都有已知的重量 $w_ e 美元, 但以某种概率独立实现 $p_ e 美元。 算法可以查询一个边缘以查看它是否实现 。 我们认为, 研究周密的查询对问题的承诺版本, 其中任何恰好实现的边缘都必须包含在解决方案中 。 Gamlath、 Kale 和 Svensson 显示, 当输入图是双边的时, 问题就承认了 $( $1 / e) o- accession。 在本文中, 我们给出的算法是绝对常数 $\ delta > 0.0014 获得 $ ( $1/ e ⁇ delta) $- approxmolmation, 从而打破了这个普遍的束缚 。