Smoothed Analysis of the Squared Euclidean Maximum-Cut Problem

It is well-known that local search heuristics for the Maximum-Cut problem can take an exponential number of steps to find a local optimum, even though they usually stabilize quickly in experiments. To explain this discrepancy we have recently analyzed the simple local search algorithm FLIP in the framework of smoothed analysis, in which inputs are subject to a small amount of random noise. We have shown that in this framework the number of iterations is quasi-polynomial, i.e., it is polynomially bounded in nlogn and φ, where n denotes the number of nodes and φ is a parameter of the perturbation.