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 $a>0$.

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