Pseudorandom sets in Grassmann graph have near-perfect expansion

Subhash Khot, Dor Minzer, Muli Safra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We prove that pseudorandom sets in the Grassmann graph have near-perfect expansion. This completes the last missing piece of the proof of the 2-to-2-Games Conjecture (albeit with imperfect completeness). The Grassmann graph has induced subgraphs that are themselves isomorphic to Grassmann graphs of lower orders. A set of vertices is called pseudorandom if its density within all such subgraphs (of constant order) is at most slightly higher than its density in the entire graph. We prove that pseudorandom sets have almost no edges within them. Namely, their edge-expansion is very close to 1.

Original languageEnglish
Title of host publicationProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
EditorsMikkel Thorup
PublisherIEEE Computer Society
Pages592-601
Number of pages10
ISBN (Electronic)9781538642306
DOIs
StatePublished - 30 Nov 2018
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: 7 Oct 20189 Oct 2018

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2018-October
ISSN (Print)0272-5428

Conference

Conference59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Country/TerritoryFrance
CityParis
Period7/10/189/10/18

Keywords

  • 2-to-2 games
  • Grassmann graph
  • PCP
  • Unique games conjecture

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