$2/3$-approximation algorithm for the maximization version of the asymmetric two peripatetic salesman problem

We present a polynomial approximation algorithm for the maximization version of the asymmetric two peripatetic salesman problem which consists in finding two edge-disjoint Hamiltonian circuits of maximum total weight in a complete weighted digraph. The algorithm guarantees an approximation ratio of $2/3$ in cubic running time. Ill. 5, bibliogr. 7.