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We prove that any polynomial‐time    α  (  n  )   ‐approximation algorithm for the   n  ‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time    O  (  α  (  C  )  )   ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where   C   is the number of weakly connected components in the subgraph induced by the positive‐demand arcs—a small number in many applications. In conjunction with known results, we obtain constant‐factor approximations for    C  ∈  O  (  log  n  )    and    O  (  log  C  /  log  log  C  )   ‐approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial‐time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on  C  and since  C  = 1 in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017

A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments