论文标题
超过$（1-1/e）$ - 加权随机匹配的近似
Beating $(1-1/e)$-Approximation for Weighted Stochastic Matching
论文作者
论文摘要
在随机加权匹配的问题中，目标是在不确定其边缘的存在时找到图形的大量匹配。特别是，每个边缘$ e $都有已知的权重$ w_e $，但在某些概率$ p_e $的情况下独立实现。该算法可能会查询边缘以查看是否实现。我们考虑了该问题的经过良好研究的查询提交版本，其中偶然实现的任何查询边缘都必须包括在解决方案中。 Gamlath，Kale和Svensson表明，当输入图是二分时时，问题承认$（1-1/e）$ - 近似。在本文中，我们给出了一种算法，即对于绝对常数$δ> 0.0014 $获得$（1-1/e+δ）$ - 近似，因此打破了这种普遍的结合。
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 $δ> 0.0014$ obtains a $(1-1/e+δ)$-approximation, therefore breaking this prevalent bound.
