### Abstract

This paper focuses on a generalization of the traveling salesman problem (TSP), called the subpath planning problem (SPP). Given 2n vertices and n independent edges on a metric space, we aim to find a shortest tour that contains all the edges. SPP is one of the fundamental problems in both artificial intelligence and robotics. Our main result is to design a 1.5-approximation algorithm that runs in polynomial time, improving the currently best approximation algorithm. The idea is direct use of techniques developed for TSP. In addition, we propose a generalization of SPP called the subgroup planning problem (SGPP). In this problem, we are given a set of disjoint groups of vertices, and we aim to find a shortest tour such that all the vertices in each group are traversed sequentially. We propose a 3-approximation algorithm for SGPP. We also conduct numerical experiments. Compared with previous algorithms, our algorithms improve the solution quality by more than 10% for large instances with more than 10,000 vertices.

Original language | English |
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Title of host publication | 26th International Joint Conference on Artificial Intelligence, IJCAI 2017 |

Publisher | International Joint Conferences on Artificial Intelligence |

Pages | 4412-4418 |

Number of pages | 7 |

ISBN (Electronic) | 9780999241103 |

Publication status | Published - 2017 |

Event | 26th International Joint Conference on Artificial Intelligence, IJCAI 2017 - Melbourne, Australia Duration: 2017 Aug 19 → 2017 Aug 25 |

### Other

Other | 26th International Joint Conference on Artificial Intelligence, IJCAI 2017 |
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Country | Australia |

City | Melbourne |

Period | 17/8/19 → 17/8/25 |

### ASJC Scopus subject areas

- Artificial Intelligence

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## Cite this

*26th International Joint Conference on Artificial Intelligence, IJCAI 2017*(pp. 4412-4418). International Joint Conferences on Artificial Intelligence.