Pattern Recognition applications deal with ever increasing datasets, both in size and complexity. In this work, we propose and analyze efficient algorithms for the Optimum-Path Forest (OPF) supervised classifier. This classifier has proven to provide results comparable to most well-know pattern recognition techniques, but with a much faster training phase. However, there is still room for improvement. The contribution of this work is the introduction of spatial indexing and parallel algorithms on the training and classification phases of the OPF supervised classifier. First, we propose a simple parallelization approach for the training phase. Following the traditional sequential training for the OPF, it maintains a priority queue to compute best samples at each iteration. Later on, we replace this priority queue by an array and a linear search, in the aim of using a more parallel-friendl...