A 5/8 approximation algorithm for the maximum asymmetric TSP

The maximum asymmetric traveling salesperson problem, also known as the taxicab rip-off problem, is the problem of finding a maximally weighted tour in a complete asymmetric graph with nonnegative weights. We propose a polynomial time approximation algorithm for the problem with a 5/8 approximation guarantee. This (1) improves upon the approximation factors of previous results and (2) presents a simpler solution to the previously fairly involved algorithms. Our solution uses a simple linear programming formulation. Previous solutions were combinatorial. We make use of the linear programming in a novel manner and strengthen the path-coloring method originally proposed in [S. R. Kosaraju, J. K. Park, and C. Stein, Long tours and short superstrings, in Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, 1994, pp. 166-177].