On the integrality Gap of Small Asymmetric Travelling Salesman Problems: A Polyhedral and Computational Approach

\(\) In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for small-sized instances. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ( \(P_{ASEP}^n\) ) and its vertices. The polytope’s … Read more

Upper Bounds on ATSP Neighborhood Size

We consider the Asymmetric Traveling Salesman Problem (ATSP) and use the definition of neighborhood by Deineko and Woeginger (see Math. Programming 87 (2000) 519-542). Let $\mu(n)$ be the maximum cardinality of polynomial time searchable neighborhood for the ATSP on $n$ vertices. Deineko and Woeginger conjectured that $\mu (n)< \beta (n-1)!$ for any constant $\beta >0$ … Read more