Classical complexity analysis for NP-hard problems is usually oriented to worst-case scenarios, considering only the asymptotic behavior. However, there are practical algorithms running in a reasonable time for many classic problems. Furthermore, there is evidence pointing towards polynomial algorithms in the linear decision tree model to solve these problems, although not explored much. In this work, we explore previous theoretical results. We show that the optimal solution for 0-1 combinatorial problems can be found by reducing these problems into a Nearest Neighbor Search over the set of corresponding Voronoi vertices. We use the hyperplanes delimiting these regions to systematically generate a decision tree that repeatedly splits the space until it can separate all solutions, guaranteeing an optimal answer. We run experiments to test the size limits for which we can build these trees for the cases of the 0-1 knapsack, weighted minimum cut, and symmetric traveling salesman. We manage to find the trees of these problems with sizes up to 10, 5, and 6, respectively. We also obtain the complete adjacency relations for the skeletons of the knapsack and traveling salesman polytopes up to size 10 and 7. Our approach consistently outperforms the enumeration method and the baseline methods for the weighted minimum cut and symmetric traveling salesman, providing optimal solutions within microseconds.