Beating Two-Thirds For Random-Order Streaming Matching

Authors Sepehr Assadi, Soheil Behnezhad

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Sepehr Assadi
  • Department of Computer Science, Rutgers University, Piscataway, NJ, USA
Soheil Behnezhad
  • Department of Computer Science, University of Maryland, College Park, MD, USA


We thank Aaron Bernstein for helpful conversations on the random-order streaming matching problem and several insightful comments that helped us in improving the presentation of the paper. We also thank the anonymous ICALP reviewers for their valuable comments.

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Sepehr Assadi and Soheil Behnezhad. Beating Two-Thirds For Random-Order Streaming Matching. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 19:1-19:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We study the maximum matching problem in the random-order semi-streaming setting. In this problem, the edges of an arbitrary n-vertex graph G = (V, E) arrive in a stream one by one and in a random order. The goal is to have a single pass over the stream, use O(n ⋅ polylog) space, and output a large matching of G. We prove that for an absolute constant ε₀ > 0, one can find a (2/3 + ε₀)-approximate maximum matching of G using O(n log n) space with high probability. This breaks the natural boundary of 2/3 for this problem prevalent in the prior work and resolves an open problem of Bernstein [ICALP'20] on whether a (2/3 + Ω(1))-approximation is achievable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Maximum Matching
  • Streaming
  • Random-Order Streaming


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