The random-field Potts model and spin-glass models are two prominent examples of NP-hard problem in statistical physics. If investigated numerically, extensive computer simulations are required to study these models. Because of the lack of efficient computational methods, the random-field Potts model has not been studied broadly yet. Here we develop an algorithm to study the random-field Potts model using a graph-cut method. It does not guarantee to find a ground state but the lowest states can be found very efficiently. We also determined the overlap of the lowest states found by the graph-cut method with the ground states found by a parallel tempering method. It is found that the lowest states found by the graph cut method have more than 80% overlap with the ground states. For the larger system sizes, the graph-cut method is much more efficient then parallel tempering method. Two-dimensional Edward-Anderson spin-glass model has been examined broadly in many previous studies. Here we focus on the phase transition of under-frustrated spin-glasses with Gaussian and bimodal couplings. There are some claims that under-frustrated two-dimensional spin-glass systems might have a spin-glass phase at finite temperatures. To study this model, we first introduce an implementation of parallel tempering and a cluster update on GPUs. The simulation results give hints that the under-frustrated spin-glass belongs to the same universality class as stochastic spin-glass and there exists no spin-glass phase at finite temperature.