a time, it can use multiple merits in the selection of pivots at the same time in a deterministic way which is different from the randomized rules. We wish that these features give us some hope to find some strong polynomial algorithms to solve linear programming problems. We may extend the proposed algorithm to select more than two entering variables, but there is a trade-off between reducing iteration numbers and reducing the cost of each iteration.

In this paper, we use small letters with bold font for vectors and capital letters with bold font for matrices. The remainder of the paper is organized as follows. Section 2 describes the proposed algorithm. Section 3 analyzes the iteration numbers of the algorithm. Section 4 provides the information on the numerical test for three variants of Klee-Minty cubes. The concluding remarks are in Section 5.

The proposed algorithm
======================

We consider the primal linear programming problem in the standard form: $$\begin{aligned}
\begin{array}{cl}
\min  &  \c^{\T}\x, \\ 
\mbox{\rm subject to} 
&  \A\x=\b, \hspace{0.1in} \x \ge \0,
\end{array}
\label{LP}\end{aligned}$$ where $\A \in {\R}^{m \times n}$, $\b \in {\R}^{m}$, $\c \in {\R}^{n}$ are given, and $\x \in {\R}^n$ is the vector to be optimized. Associated with 