The Tsp and the Sum of its Marginal Values

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.

• Type: Journal
• Year: 2006
• Where: IJCGA
• Authors: Moshe Dror, Yusin Lee, James B. Orlin, Valentin Polishchuk
• Keywords: IJCGA 2006, Marginal Value, Traveling Salesperson Problem, TSP Ratio