one vertex to the next vertex along an edge of the polytope. Therefore, the diameter of a polytope, defined as the shortest path or the least number of edges between any two vertices of the polytope, is the smallest number of iterations that the best simplex algorithm can possibly achieve. Hirsch in 1957 [@dantzig63] conjectured that the diameter of the polytope is $m-n$ for the polytope $P=\{ \x\in \R^n: \A\x \le \b \}$ where $\A \in \Z^{m \times n}$ and $m>n$. This conjecture was disapproved by Santos [@santos12] after $50$ years worth of efforts of many experts. Now, some experts, for example Santos [@santos12a], believe that the diameter of the convex polytope can be bounded by a polynomial of $(m-n)n$. This new conjecture of the bound for the diameter of the convex polytope is far away from the best-known quasi-polynomial upper bounds which are due to Kalai and Kleitman [@kalai92], Todd [@todd14], and Sukegawa [@sukegawa17]. In a recent effort [@yang18], this author showed that for a given polytope, the diameter is bounded by $\mathcal{O} \left( \frac{n^3 \Delta}{\det(\A^*)} \right)$, where $\Delta$ is the largest absolute value among all $(n-1) \times (n-1)$ sub-determinants of $\A$ and ${\det(\A^*)}$ is the smallest absolute value 