Pseudorandom sets in Grassmann graph have near-perfect expansion

Subhash Khot, Dor Minzer, Muli Safra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 (US)
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
Volume2018-October
ISBN (Electronic)9781538642306
DOIs
StatePublished - Nov 30 2018
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: Oct 7 2018Oct 9 2018

Other

Other59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
CountryFrance
CityParis
Period10/7/1810/9/18

Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Khot, S., Minzer, D., & Safra, M. (2018). Pseudorandom sets in Grassmann graph have near-perfect expansion. In M. Thorup (Ed.), Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 (Vol. 2018-October, pp. 592-601). [8555140] IEEE Computer Society. https://doi.org/10.1109/FOCS.2018.00062

Pseudorandom sets in Grassmann graph have near-perfect expansion. / Khot, Subhash; Minzer, Dor; Safra, Muli.

Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018. ed. / Mikkel Thorup. Vol. 2018-October IEEE Computer Society, 2018. p. 592-601 8555140.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Khot, S, Minzer, D & Safra, M 2018, Pseudorandom sets in Grassmann graph have near-perfect expansion. in M Thorup (ed.), Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018. vol. 2018-October, 8555140, IEEE Computer Society, pp. 592-601, 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018, Paris, France, 10/7/18. https://doi.org/10.1109/FOCS.2018.00062
Khot S, Minzer D, Safra M. Pseudorandom sets in Grassmann graph have near-perfect expansion. In Thorup M, editor, Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018. Vol. 2018-October. IEEE Computer Society. 2018. p. 592-601. 8555140 https://doi.org/10.1109/FOCS.2018.00062
Khot, Subhash ; Minzer, Dor ; Safra, Muli. / Pseudorandom sets in Grassmann graph have near-perfect expansion. Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018. editor / Mikkel Thorup. Vol. 2018-October IEEE Computer Society, 2018. pp. 592-601
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