The Asymmetric Traveling Salesman Problem
Howard Kleiman
Abstract
Starting with M(a), an n X n asymmetric cost matrix, Jonker and Volgenannt transformed it into a 2n X 2n symmetric cost matrix, M(s)where M(s) has unusual properties. One such property is that an optimal tour in M(s) yields an optimal tour in M(a). Modifying M(s), we apply the modified Floyd-Warshall algorithm to M(s). Due to the structure of M(s), we hopefully)can always obtain an optimal tour in M(a) in polynomial time.If theorem 1 in this paper is valid, since the asymmetric traveling salesman problem is NP-hard, P would equal NP.
Create a lesson
Related papers
A Note on the Measure of Vector and Pythagorean Theorem
Yu. V. Brezhnev
On Weighted Convex Graphs
Angshuman R. Goswami
On characterizations, Decompositions, and Stability of Convex Sequences
Angshuman R. Goswami
New Laplace convolution integrals involving exponential, error, and parabolic cylinder functions with applications in heat transfer and linear viscoelasticity
González Santander, Juan Luis
Resolution of Singularities in Positive Characteristic: Frobenius-Hasse Towers and Exceptional-History Descent
Chenxiao Tian
Information Geometry (IG) Lives at Edge or Boundary of SMG (statistically meaningful geometry): - the First Edge Theorem and Applications
Bing Cheng, Yi-Shuai Niu, Howell Tong et al.