## Abstract

In this paper, we consider the a priori traveling salesman problem (TSP) in the scenario model. In this problem, we are given a list of subsets of the vertices, called scenarios, along with a probability for each scenario. Given a tour on all vertices, the resulting tour for a given scenario is obtained by restricting the solution to the vertices of the scenario. The goal is to find a tour on all vertices that minimizes the expected length of the resulting restricted tour. We show that this problem is already NP-hard and APX-hard when all scenarios have size four. On the positive side, we show that there exists a constant-factor approximation algorithm in three restricted cases: if the number of scenarios is fixed, if the number of missing vertices per scenario is bounded by a constant, and if the scenarios are nested. Finally, we discuss an elegant relation with an a priori minimum spanning tree problem.

Original language | English |
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Title of host publication | Approximation and Online Algorithms |

Subtitle of host publication | 14th International Workshop, WAOA 2016, Revised Selected Papers |

Editors | Klaus Jansen, Monaldo Mastrolilli |

Place of Publication | Cham |

Publisher | Springer |

Pages | 183-196 |

Number of pages | 14 |

ISBN (Electronic) | 978-3-319-51741-4 |

ISBN (Print) | 978-3-319-51740-7 |

DOIs | |

Publication status | Published - 2017 |

Event | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 - Aarhus, Denmark Duration: 25 Aug 2016 → 26 Aug 2016 Conference number: 14 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 10138 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Workshop

Workshop | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 |
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Abbreviated title | WAOA |

Country/Territory | Denmark |

City | Aarhus |

Period | 25/08/16 → 26/08/16 |

## Keywords

- Traveling salesman problem
- A priori optimization
- Master tour
- Optimization under scenarios

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