“…The higher-order binary Markov random field (HoMRF) is a non-convex optimization model widely used in the fields of economy, information theory, quantum computing, machine learning and image analysis [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ]. Recently, a new order reduction method has been developed to optimize HoMRF energies.…”