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

TL;DR

This paper presents a simple, efficient algorithm that approximates the maximum matching size within 0.5109 in sublinear time, significantly improving over prior methods with minimal complexity.

Contribution

It introduces a novel, simpler algorithm achieving a 0.5109-approximation for maximum matching in sublinear time, surpassing previous marginal improvements.

Findings

Achieves a 0.5109-approximation in  O(nsqrt{n}) time.

Improves over prior algorithms with marginal gains over 0.5.

Simpler approach compared to existing methods.

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.