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arXiv · 2506.01669

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time

Sepideh Mahabadi·Mohammad Roghani·Jakub Tarnawski
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Abstract

We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation algorithm with a running time of $\tilde{O}(n\sqrt{n})$. All previous algorithms either provide only a marginal improvement (e.g., $2^{-280}$) over the $0.5$-approximation that arises from estimating a \emph{maximal} matching, or have a running time that is nearly $n^2$. Our approach is also arguably much simpler than other algorithms beating $0.5$-approximation.

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Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski. 2025-06-02. A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time. https://arxiv.org/abs/2506.01669

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