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REPORTS > KEYWORD > UNIQUE GAME CONJECTURE:
Reports tagged with Unique Game Conjecture:
TR15-058 | 1st April 2015
Peng Cui

#### Strengthened Hardness for Approximating Minimum Unique Game and Small Set Expansion

In this paper, the author puts forward a variation of Feige's Hypothesis, which claims that it is hard on average refuting Unbalanced Max 3-XOR under biased assignments on a natural distribution. Under this hypothesis, the author strengthens the previous known hardness for approximating Minimum Unique Game, $5/4-\epsilon$, by proving that ... more >>>

TR18-006 | 10th January 2018
Subhash Khot, Dor Minzer, Muli Safra

#### Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion

Revisions: 2

We prove that pseudorandom sets in Grassmann graph have near-perfect expansion as hypothesized in [DKKMS-2]. This completes
the proof of the $2$-to-$2$ Games Conjecture (albeit with imperfect completeness) as proposed in [KMS, DKKMS-1], along with a
contribution from [BKT].

The Grassmann graph $Gr_{global}$ contains induced subgraphs $Gr_{local}$ that are themselves ... more >>>

TR18-034 | 15th February 2018
Young Kun Ko

#### On Symmetric Parallel Repetition : Towards Equivalence of MAX-CUT and UG

Unique Games Conjecture (UGC), proposed by [Khot02], lies in the center of many inapproximability results. At the heart of UGC lies approximability of MAX-CUT, which is a special instance of Unique Game.[KhotKMO04, MosselOO05] showed that assuming Unique Games Conjecture, it is NP-hard to distinguish between MAX-CUT instance that has a ... more >>>

TR18-077 | 23rd April 2018
Boaz Barak, Pravesh Kothari, David Steurer

#### Small-Set Expansion in Shortcode Graph and the 2-to-2 Conjecture

Dinur, Khot, Kindler, Minzer and Safra (2016) recently showed that the (imperfect completeness variant of) Khot's 2 to 2 games conjecture follows from a combinatorial hypothesis about the soundness of a certain Grassmanian agreement tester''.
In this work, we show that the hypothesis of Dinur et al follows from a ... more >>>

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