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unique games conjecture : ウィキペディア英語版
unique games conjecture

In computational complexity theory, the Unique Games Conjecture is a conjecture made by Subhash Khot in 2002.〔
〕〔
〕〔 The conjecture postulates that the problem of determining the approximate ''value'' of a certain type of game, known as a ''unique game'', has NP-hard algorithmic complexity. It has broad applications in the theory of hardness of approximation. If it is true, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem), but also impossible to get a good polynomial-time approximation. The problems for which such an inapproximability result would hold include constraint satisfaction problems which crop up in a wide variety of disciplines.
The conjecture is unusual in that the academic world seems about evenly divided on whether it is true or not.〔
==Formulations==

The unique games conjecture can be stated in a number of equivalent ways.

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