License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.19
URN: urn:nbn:de:0030-drops-140887
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14088/
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Assadi, Sepehr ; Behnezhad, Soheil

Beating Two-Thirds For Random-Order Streaming Matching

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LIPIcs-ICALP-2021-19.pdf (1 MB)

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.

BibTeX - Entry

@InProceedings{assadi_et_al:LIPIcs.ICALP.2021.19,
  author =	{Assadi, Sepehr and Behnezhad, Soheil},
  title =	{{Beating Two-Thirds For Random-Order Streaming Matching}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{19:1--19:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14088},
  URN =		{urn:nbn:de:0030-drops-140887},
  doi =		{10.4230/LIPIcs.ICALP.2021.19},
  annote =	{Keywords: Maximum Matching, Streaming, Random-Order Streaming}
}

Keywords: Maximum Matching, Streaming, Random-Order Streaming
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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