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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.51
URN: urn:nbn:de:0030-drops-94555
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9455/
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Li, Xin ; Lovett, Shachar ; Zhang, Jiapeng

Sunflowers and Quasi-Sunflowers from Randomness Extractors

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Abstract

The Erdös-Rado sunflower theorem (Journal of Lond. Math. Soc. 1960) is a fundamental result in combinatorics, and the corresponding sunflower conjecture is a central open problem. Motivated by applications in complexity theory, Rossman (FOCS 2010) extended the result to quasi-sunflowers, where similar conjectures emerge about the optimal parameters for which it holds. In this work, we exhibit a surprising connection between the existence of sunflowers and quasi-sunflowers in large enough set systems, and the problem of constructing (or existing) certain randomness extractors. This allows us to re-derive the known results in a systematic manner, and to reduce the relevant conjectures to the problem of obtaining improved constructions of the randomness extractors.

BibTeX - Entry

@InProceedings{li_et_al:LIPIcs:2018:9455,
  author =	{Xin Li and Shachar Lovett and Jiapeng Zhang},
  title =	{{Sunflowers and Quasi-Sunflowers from Randomness Extractors}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{51:1--51:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9455},
  URN =		{urn:nbn:de:0030-drops-94555},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.51},
  annote =	{Keywords: Sunflower conjecture, Quasi-sunflowers, Randomness Extractors}
}

Keywords: Sunflower conjecture, Quasi-sunflowers, Randomness Extractors
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 02.08.2018


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