Janos Barta The integrality gap of the subtour elimination relaxation for the Traveling Salesman Problem is a longstanding open problem, epitomized by the \(\frac{4}{3}\)-conjecture. Understanding this gap requires a detailed analysis of the extreme points of the subtour elimination polytope. In this work, we introduce a new perspective for studying the integrality gap through what we call … Read more
We address the classical Dantzig – Fulkerson – Johnson formulation of the symmetric metric Traveling Salesman Problem and study the integrality gap of its linear relaxation, namely the Subtour Elimination Problem (SEP). This integrality gap is conjectured to be 4/3. We prove that, when solving a problem on n nodes, if the optimal SEP solution … Read more
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 instances with n nodes, where n is small. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ($P^{n}_{ASEP}$) and its vertices. The … Read more