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arXiv · 2307.02968

A Simple $(1-\epsilon)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching

Sepehr Assadi
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Abstract

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.

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Sepehr Assadi. 2023-07-06. A Simple $(1-\epsilon)$-Approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching. https://doi.org/10.46298/theoretics.25.16

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