Solving the max-cut problem using eigenvalues Original Research Article

We present computational experiments for solving the max-cut problem using an eigenvalue relaxation. Our motivatiòn is twofold — we are interested both in the quality of the bound, and in developing an efficient code to compute it. We describe the theoretical background of the method, an implementation of the algorithm, and its practical performance. The experiments have been done for various data sets, including random graphs of different densities, clustering problems, problems arising from quadratic 0–1 optimization, and some graphs taken from the literature. The basic algorithm is used to compute an upper and lower bound on the max-cut. The relative gap between these bounds is typically much less than 10%. We also present results where the basic algorithm is used in a “branch and bound” setting to find the exact value of the max-cut. The largest problems solved to optimality are dense geometric graphs with up to 100 nodes.