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.
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