From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization

We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP. The parameters we consider respective generalizations are upper bounded by number of asymmetric distances, which yields algorithms efficiently compute good also moderately TSP instances. As generalization algorithm, derive a 2.5-approximation, where parameter is size vertex cover subgraph induced distances. Our gives 3-approximation, minimum distances in spanning arborescence. Further, combine these with notion symmetry relaxation allows trade approximation guarantee runtime. Since two theoretically incomparable, present experimental results show that generalized frequently outperforms respect size.