We consider an APX-hard variant (∆-Max-ATSP) and an APX-hard relaxation (Max-3-DCC) of the classical traveling salesman problem. We present a 31 40-approximation algorithm for ∆-Max-ATSP and a 3 4-approximation algorithm for Max-3-DCC with polynomial running time. The results are obtained via a new way of applying techniques for computing undirected cycle covers to directed problems. Key words: Approximation algorithm, Traveling Salesman Problem, cycle cover, blossom inequalities.
Markus Bläser, L. Shankar Ram, Maxim Sviriden