### Abstract

We present a near-optimal polynomial-time approximation algorithm for the asymmetric traveling salesman problem for graphs of bounded orientable or non-orientable genus. Given any algorithm that achieves an approximation ratio of f (n) on arbitrary n-vertex graphs as a black box, our algorithm achieves an approximation factor of O( f (g)) on graphs with genus g. In particular, the O(log n= log log n)-approximation algorithm for general graphs by Asadpour et al. [SODA 2010] immediately implies an O(log g= log log g)-approximation algorithm for genus-g graphs. Moreover, recent results on approximating the genus of graphs imply that our O(log g= log log g)-approximation algorithm can be applied to bounded-degree graphs even if no genus-g embedding of the graph is given. Our result improves and generalizes the O(√g log g)-approximation algorithm of Oveis Gharan and Saberi [SODA 2011], which applies only to graphs with orientable genus g and requires a genus-g embedding as part of the input, even for bounded-degree graphs. Finally, our techniques yield a O(1)-approximation algorithm for ATSP on graphs of genus g with running time 2^{O(g)}· n^{O(1)}

Original language | English (US) |
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Title of host publication | Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014 |

Publisher | Association for Computing Machinery |

Pages | 130-135 |

Number of pages | 6 |

ISBN (Print) | 9781450325943 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan Duration: Jun 8 2014 → Jun 11 2014 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 30th Annual Symposium on Computational Geometry, SoCG 2014 |
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Country | Japan |

City | Kyoto |

Period | 6/8/14 → 6/11/14 |

### Fingerprint

### Keywords

- Approximation algorithms
- Topological graph algorithms
- Traveling salesman

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014*(pp. 130-135). (Proceedings of the Annual Symposium on Computational Geometry). Association for Computing Machinery. https://doi.org/10.1145/2582112.2582136