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We provide $\widetilde{O}(\epsilon^{-1})$-pass semi-streaming algorithms forcomputing $(1-\epsilon)$-approximate maximum cardinality matchings in bipartitegraphs. 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 Guha. To obtain ourresults we provide semi-streaming adaptations of more general continuousoptimization tools. Further, we leverage these techniques to obtainimprovements for streaming variants of approximate linear programming, optimaltransport, exact matching, transshipment, and shortest path problems.

Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space