Approximating asymmetric maximum TSP

The asymmetric maximim traveling salesman problem, also known as the Taxicab Ripoff problem, is the problem of finding a maximally weighted tour in a complete asymmetric graph with non-negative weights. Interesting in its own right, this problem is also motivated by such problems such as the shortest superstring problem. 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 LP formulation. Previous solutions where combinatorial. We make use of the LP in a novel manner and strengthen the Path-Coloring method originally proposed in [13].