Ariadne: An algorithm for computing a maximum clique in polynomial time

In this paper, we present a polynomial-time algorithm for the maximum clique problem, which implies P = NP. Our algorithm is based on a continuous game-theoretic representation of this problem and at its heart lies a discrete-time dynamical system. The iterates of our dynamical system are guaranteed to converge to a fixed point that is not necessarily an equilibrium but we show that a maximum clique can be computed enter a neighborhood of a fixed point.