On Rich 2-to-1 Games

Authors Mark Braverman, Subhash Khot, Dor Minzer

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Author Details

Mark Braverman
  • Department of Computer Science, Princeton University, NJ, USA
Subhash Khot
  • Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, NY, USA
Dor Minzer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

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Mark Braverman, Subhash Khot, and Dor Minzer. On Rich 2-to-1 Games. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We propose a variant of the 2-to-1 Games Conjecture that we call the Rich 2-to-1 Games Conjecture and show that it is equivalent to the Unique Games Conjecture. We are motivated by two considerations. Firstly, in light of the recent proof of the 2-to-1 Games Conjecture [Subhash Khot et al., 2017; Irit Dinur et al., 2018; Irit Dinur et al., 2018; Subhash Khot et al., 2018], we hope to understand how one might make further progress towards a proof of the Unique Games Conjecture. Secondly, the new variant along with perfect completeness in addition, might imply hardness of approximation results that necessarily require perfect completeness and (hence) are not implied by the Unique Games Conjecture.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • PCP
  • Unique-Games
  • Perfect Completeness


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