MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

Abstract We present , a parallel semidefinite-based exact solver for Max-Cut, problem of finding the cut with maximum weight in given graph. The algorithm uses branch and bound paradigm that applies alternating direction method multipliers as bounding routine to solve basic semidefinite relaxation strengthened by subset hypermetric inequalities. benefit new approach is less computationally expensive update rule dual variable respect inequality constraints. provide theoretical convergence well extensive computational experiments this method, show our outperforms state-of-the-art approaches. Furthermore, combining algorithmic ingredients from serial algorithm, we develop an efficient distributed based on MPI.