## Abstract

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.

Original language | English |
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Pages (from-to) | 262-278 |

Number of pages | 17 |

Journal | Networks |

Volume | 70 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Oct 2017 |

## Keywords

- Chinese Postman
- combinatorial optimization
- fixed-parameter algorithm
- NP-hard problem
- Rural Postman
- transportation
- vehicle routing
- EULERIAN EXTENSION
- BOUNDS