We present a simple semi-streaming algorithm for $(1-\epsilon)$-approximation of bipartite matching in $O(\log{\!(n)}/\epsilon)$ passes. This matches the performance of state-of-the-art "$\epsilon$-efficient" algorithms -- the ones with much better dependence on $\epsilon$ albeit with some mild dependence on $n$ -- while being considerably simpler. The algorithm relies on a direct application of the multiplicative weight update method with a self-contained primal-dual analysis that can be of independent interest. To show case this, we use the same ideas, alongside standard tools from matching theory, to present an equally simple semi-streaming algorithm for $(1-\epsilon)$-approximation of weighted matchings in general (not necessarily bipartite) graphs, again in $O(\log{\!(n)}/\epsilon)$ passes.

翻译：我们提出了一种简单的半流式算法，用于在$O(\log(n)/\varepsilon)$轮次内实现二分图匹配的$(1-\epsilon)$近似。该算法在性能上与最先进的“$\epsilon$-高效”算法相当——这些算法虽然对$\epsilon$有更优的依赖关系，但对$n$存在轻微依赖——同时更简洁。该算法直接应用了乘法权重更新方法，并辅以自洽的原-对偶分析，这种分析本身可能具有独立研究价值。为展示其通用性，我们利用相同思路，结合匹配理论的标准工具，提出了另一种同样简单的半流式算法，用于一般图（不限于二分图）加权匹配的$(1-\epsilon)$近似，同样在$O(\log(n)/\varepsilon)$轮次内完成。