We provide $\widetilde{O}(\epsilon^{-1})$-pass semi-streaming algorithms for computing $(1-\epsilon)$-approximate maximum cardinality matchings in bipartite graphs. Our most efficient methods are deterministic and use optimal, $O(n)$, space, improving upon the space complexity of the previous state-of-the-art $\widetilde{O}(\epsilon^{-1})$-pass algorithm of Ahn and Gupta. To obtain our results we provide semi-streaming adaptations of more general continuous optimization tools. Further, we leverage these techniques to obtain improvements for streaming variants of approximate linear programming, optimal transport, exact matching, transshipment, and shortest path problems.
翻译：我们提供$\全局性{O}(\\ epsilon}-1}(\\ epsilon}-1})$pass 半流算法,用于计算(1-\ epsilon)$($1-epsilon)$-近似最大基点对齐的双面图形。我们最有效的方法是确定并使用最佳的,美元(n)$(o)$(o),空间,改进Ahn和Gupta以前最先进的全局性($\ epsilon}(\\\ ilsilon}-1})$($) pass-passion 运算法的空间复杂性。为了获得我们的成果,我们提供更普遍的连续优化工具的半流适应。此外,我们利用这些技术来改进近似线性编程、最优化的运输、精确匹配、转运和最短路径问题的流变。
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