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

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Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski

Published: 2025, Last Modified: 08 Dec 2025ICALP 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
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 Õ(n√n). All previous algorithms either provide only a marginal improvement (e.g., 2^{-280}) over the 0.5-approximation that arises from estimating a maximal matching, or have a running time that is nearly n². Our approach is also arguably much simpler than other algorithms beating 0.5-approximation.