### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

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

**An improved approximation algorithm for the subpath planning problem and its generalization.** / Sumita, Hanna; Yonebayashi, Yuma; Kakimura, Naonori; Kawarabayashi, Ken Ichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*26th International Joint Conference on Artificial Intelligence, IJCAI 2017.*International Joint Conferences on Artificial Intelligence, pp. 4412-4418, 26th International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, 17/8/19.

}

TY - GEN

T1 - An improved approximation algorithm for the subpath planning problem and its generalization

AU - Sumita, Hanna

AU - Yonebayashi, Yuma

AU - Kakimura, Naonori

AU - Kawarabayashi, Ken Ichi

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85031939112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031939112&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85031939112

SP - 4412

EP - 4418

BT - 26th International Joint Conference on Artificial Intelligence, IJCAI 2017

PB - International Joint Conferences on Artificial Intelligence

ER -