Let the costs $C(i,j)$ for an instance of the asymmetric traveling salesperson problem be independent uniform $[0,1]$ random variables. We consider the efficiency of branch and bound algorithms that use the assignment relaxation as a lower bound. We show that w.h.p. the number of steps taken in any such branch and bound algorithm is $e^{\Omega(n^a)}$ for some small absolute constant $a>0$.

翻译：设非对称旅行商问题实例中的成本$C(i,j)$为独立的$[0,1]$均匀随机变量。我们考虑采用指派松弛作为下界的分支定界算法的效率。我们证明，对于任意此类分支定界算法，其步骤数以高概率达到$e^{\Omega(n^a)}$，其中$a>0$为某个较小的绝对常数。