On Khot's unique games conjecture

Abstract

In 2002, Subhash Khot formulated the Unique Games Conjecture, a conjecture about the computational complexity of certain optimization problems. The conjecture has inspired a remarkable body of work, which has clarified the computational complexity of several optimization problems and the effectiveness of "semidefinite programming" convex relaxations. In this paper, which assumes no prior knowledge of computational complexity, we describe the context and statement of the conjecture, and we discuss in some detail one specific line of work motivated by it. © 2011 American Mathematical Society.