Solving a Random Asymmetric TSP Exactly in Quasi-Polynomial Time w.h.p

Abstract: Let the costs $C(i,j)$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent copies of an random variable $C$ that (i) satisfies $\Pr(C\geq x)=1-x+O(x^2)$ as $x\to 0$ and (ii) has an exponential tail. We describe an algorithm that solves ATSP exactly in time $e^{\log^{2+o(1)}n}$, w.h.p.