On non-optimally expanding sets in Grassmann graphs

Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer*, Muli Safra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the structure of non-expanding sets in the Grassmann graph. We put forth a hypothesis stating that every small set whose expansion is smaller than 1–δ must be correlated with one of a specified list of sets which are isomorphic to smaller Grassmann graphs. We develop a framework of Fourier analysis for analyzing functions over the Grassmann graph, and prove that our hypothesis holds for all sets whose expansion is below 3/4. Our work is motivated by [DKK+18], wherein the authors show that a linearity agreement hypothesis implies an NP-hardness gap of 1/2–ε vs. ε for Unique Games and other inapproximability results. Barak, Kothari and Steurer show that the hypothesis in this work implies the linearity agreement hypothesis [DKK+18]. Following initial publication of this work, our hypothesis was proved in [KMS18].

Original languageAmerican English
Pages (from-to)377-420
Number of pages44
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Jun 2021

Bibliographical note

Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.


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