On the integrality ratio for asymmetric TSP

The traveling salesman problem comes in two variants. The symmetric version (STSP) assumes that the cost c_ij of going to city i to city j is equal to c_ji, while the more general asymmetric version (ATSP) does not make this assumption. In both cases, it is usually assumed that we are in the metric case, i.e., the costs satisfy the triangle inequality: c_ij + c_jk ≥ c_ik for all i, j, k. In this assumption, we improve the lower bound on the integrality ratio of the Held-Karp bound for asymmetric TSP (with triangle inequality) from 4/3 to 2.