Suppose you have a complete bipartite network $G=(UV,E)$ such that $|U|=|V|,$ that has a bipartite triangle inequality $($i$.$e$.c_{ij}{c}_{i{j}^{\text{'}}}+c_{i^{\text{'}}{j}^{\text{'}}}+c_{i^{\text{'}}j}$ for all $i,i^{\text{'}},j^{\text{'}},j).$ Describe an efficient $\frac{5}{2}$ approximation algorithm for solving the this problem.

Hint If we had an efficient algorithm for solving the standard metric TSP optimally, we'd have a factor $2$ approximation for the problem.