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

Authors Sepideh Mahabadi , Mohammad Roghani , Jakub Tarnawski

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ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Sublinear Algorithms
  • Maximum Matching
  • Maximal Matching
  • Approximation Algorithm

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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 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.

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Sepideh Mahabadi, Mohammad Roghani, and Jakub Tarnawski. A 0.51-Approximation of Maximum Matching in Sublinear n^{1.5} Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 116:1-116:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.116

Author Details

Sepideh Mahabadi
  • Microsoft Research, Redmond, WA, USA
Mohammad Roghani
  • Stanford University, CA, USA
Jakub Tarnawski
  • Microsoft Research, Redmond, WA, USA

Acknowledgements

This work was done while Mohammad Roghani was an intern at Microsoft Research. The work was conducted in part while Sepideh Mahabadi was long-term visitor at the Simons Institute for the Theory of Computing as part of the Sublinear Algorithms program.

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