Fast Population Game Dynamics for Dominant Sets and Other Quadratic Optimization Problems

Abstract

We propose a fast population game dynamics, motivated by the analogy with infection and immunization processes within a population of players, for finding dominant sets, a powerful graph-theoretical notion of a cluster. Each step of the proposed dynamics is shown to have a linear time/space complexity and we show that, under the assumption of symmetric affinities, the average population payoff is strictly increasing along any non-constant trajectory, thereby allowing us to prove that dominant sets are asymptotically stable (i.e., attractive) points for the proposed dynamics. The approach is general and can be applied to a large class of quadratic optimization problems arising in computer vision. Experimentally, the proposed dynamics is found to be orders of magnitude faster than and as accurate as standard algorithms.