A parameterized approximation algorithm for the mixed and windy Capacitated Arc Routing Problem: theory and experiments - René van Bevern; Komusiewicz, Christian; Sorge, Manuel (arXiv.org, 2016)
We prove that any polynomial-time \(\alpha(n)\)-approximation algorithm for the \(n\)-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time \(O(\alpha(C))\)-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 \(C\in O(\log n)\) 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.