Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space

TL;DR

This paper introduces efficient semi-streaming algorithms for approximate maximum bipartite matching that use fewer passes and optimal space, advancing the state-of-the-art in streaming graph algorithms.

Contribution

The paper presents deterministic semi-streaming algorithms with optimal space complexity for approximate bipartite matching, improving upon previous methods and extending to other optimization problems.

Findings

Deterministic algorithms with $ ilde{O}(rac{1}{})$-pass complexity.

Optimal $O(n)$ space usage for approximate matchings.

Extensions to linear programming, transport, and shortest path problems.

Abstract

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 Guha. 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.