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Beating Two-Thirds For Random-Order Streaming Matching

Authors Sepehr Assadi, Soheil Behnezhad

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Author Details

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

Funding

  • Assadi, Sepehr: Research supported in part by the NSF CAREER award CCF-2047061 and a gift from Google Research.
  • Behnezhad, Soheil: Research supported by Google Ph.D. Fellowship.

Acknowledgements

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ICALP.2021.19

Abstract

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
Keywords
  • Maximum Matching
  • Streaming
  • Random-Order Streaming

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References

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