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Unique Games Conjecture by 2030


The Unique Games Conjecture (UGC) is a conjecture made by Nevanlinna Prize winner Subhash Khot of NYU in 2002. It states that the Unique Games problem is NP-hard, and is one of the famous open problems in computational complexity theory. It especially has implications in hardness of approximation; for instance, it implies that the problem of approximating maximum cut for graphs by a better constant than given by the Goemans-Williamson algorithm is NP-hard.

At the 2019-2020 Tel Aviv Theory Fest, MIT professor Elchanan Mossel and NYU professor and Khot made a bet that a correct proof of UGC will be uploaded to arXiv by 2030. In early 2018, Khot, along with Dor Minzer and Muli Safra, made a significant advance toward proving UGC in a paper. Harvard professor Boaz Barak agreed to referee the bet.

Will the Unique Games Conjecture be proved by 2030?

This question resolves positively if Boaz Barak writes publicly (on Twitter, a blog, or elsewhere) that Elchanan Mossel has won the bet. It resolves negatively if he announces Subhash Khot has won. If there is no announcement by the resolve date, then it resolves positively if there is a peer reviewed paper that was originally uploaded to the ArXiv in 2030 which is accepted in a major mathematics journal or computer science conference by the resolve date. Else, it resolves negatively.

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