关于$\{0,1/2\}$ -闭包的完整性和完全对偶完整性的复杂性
On the Complexity of Recognizing Integrality and Total Dual Integrality of the $\{0,1/2\}$-Closure
摘要：
有理多面体$\{ x \colon Ax \le b \}$的$\{0,\frac{1}{2}\}$ -闭包是通过在$\{0,\frac{1}{2}\}$中使用乘子将所有可以从线性系统$Ax \le b$导出的Gomory-Chvátal割相加得到的。我们表明，决定是否$\{0,\frac{1}{2}\}$ -封闭符合整数壳是强NP-困难的。我们证明的一个直接结果是，测试是否从$Ax \le b$导出的$\{0,\frac{1}{2}\}$ -闭包的线性描述是完全对偶积分，是强NP-困难的。
英文摘要：
The $\{0,\frac{1}{2}\}$-closure of a rational polyhedron $\{ x \colon Ax \le b \}$ is obtained by adding all Gomory-Chvátal cuts that can be derived from the linear system $Ax \le b$ using multipliers in $\{0,\frac{1}{2}\}$. We show that deciding whether the $\{0,\frac{1}{2}\}$-closure coincides with the integer hull is strongly NP-hard. A direct consequence of our proof is that, testing whether the linear description of the $\{0,\frac{1}{2}\}$-closure derived from $Ax \le b$ is totally dual integral, is strongly NP-hard.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
