Unique Games Conjecture
The Unique Games Conjecture is a hypothesis in theoretical computer science proposed by Subhash Khot in 2002. It suggests that certain optimization problems, specifically those involving unique games, are hard to solve efficiently. In these games, each player can choose a strategy that maximizes their score based on the choices of other players, and the conjecture posits that finding the best overall strategy is computationally difficult.
If the Unique Games Conjecture is true, it has significant implications for the field of approximation algorithms. It would mean that for many problems, no efficient algorithm can guarantee a solution close to the optimal one. This conjecture has spurred extensive research and debate within the computer science community.