This paper introduces a new notion related to the traveling salesperson problem (TSP) -the notion of the TSP ratio. The TSP ratio of a TSP instance I is the sum of the marginal values of the nodes of I divided by the length of the optimal TSP tour on I, where the marginal value of a node i I is the difference between the length of the optimal tour on I and the length of the optimal tour on I \ i. We consider the problem of establishing exact upper and lower bounds on the TSP ratio. To our knowledge, this problem has not been studied previously.
Moshe Dror, Yusin Lee, James B. Orlin, Valentin Po