Before revision:  In our experiments with several graphs, when we consider only minimal separators which are no larger than treewidth, we can significantly speed up the decomposition while still have an optimal treedepth decomposition. By the conjecture, we solve more instances than any algorithm submitted to PACE 2020. Theoretically, we prove that the conjecture for many classes of graphs. We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
After revision:  In those algorithms, although a number of minimal separators are enumerated, the minimal separators that are used for an optimal solution are empirically very small. Therefore, analyzing the upper bound on the size of minimal separators is an important problem because it has the potential to significantly reduce the computation time. A minimal separator S is called an optimal top separator if td(G) = |S| + 1 when tw is the treewidth\le .