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

TL;DR

This paper presents an algorithm that solves the asymmetric traveling salesman problem exactly in quasi-polynomial time with high probability, for instances with costs drawn from certain random distributions.

Contribution

It introduces a novel algorithm that achieves exact solutions for ATSP in quasi-polynomial time under specific random cost assumptions.

Findings

Algorithm solves ATSP exactly in $e^{ ext{polylog}(n)}$ time.

Works for costs from distributions including uniform and exponential.

High probability guarantees on solution correctness.

Abstract

Let the costs $C(i,j)$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent copies of a non-negative random variable $C$ from a class of distributions that include the uniform $[0,1]$ distribution and the exponential mean 1 distribution with mean 1. We describe an algorithm that solves ATSP exactly in time $e^{\log^{2+o(1)}n}$, w.h.p.