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.ITCS.2022.104
URN: urn:nbn:de:0030-drops-157004
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15700/
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Lovett, Shachar ; Meka, Raghu ; Mertz, Ian ; Pitassi, Toniann ; Zhang, Jiapeng

Lifting with Sunflowers

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LIPIcs-ITCS-2022-104.pdf (0.9 MB)

Abstract

Query-to-communication lifting theorems translate lower bounds on query complexity to lower bounds for the corresponding communication model. In this paper, we give a simplified proof of deterministic lifting (in both the tree-like and dag-like settings). Our proof uses elementary counting together with a novel connection to the sunflower lemma.
In addition to a simplified proof, our approach opens up a new avenue of attack towards proving lifting theorems with improved gadget size - one of the main challenges in the area. Focusing on one of the most widely used gadgets - the index gadget - existing lifting techniques are known to require at least a quadratic gadget size. Our new approach combined with robust sunflower lemmas allows us to reduce the gadget size to near linear. We conjecture that it can be further improved to polylogarithmic, similar to the known bounds for the corresponding robust sunflower lemmas.

BibTeX - Entry

@InProceedings{lovett_et_al:LIPIcs.ITCS.2022.104,
  author =	{Lovett, Shachar and Meka, Raghu and Mertz, Ian and Pitassi, Toniann and Zhang, Jiapeng},
  title =	{{Lifting with Sunflowers}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{104:1--104:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15700},
  URN =		{urn:nbn:de:0030-drops-157004},
  doi =		{10.4230/LIPIcs.ITCS.2022.104},
  annote =	{Keywords: Lifting theorems, communication complexity, combinatorics, sunflowers}
}

Keywords: Lifting theorems, communication complexity, combinatorics, sunflowers
Collection: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue Date: 2022
Date of publication: 25.01.2022

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