### 抄録

Given n robots and n target points on the plane, the minimum set cover formation (SCF) problem requires the robots to form a set cover by the minimum number of robots. In previous formation problems by mobile robots, such as gathering and pattern formation, the problems consist only of the mobile robots, and there are no points fixed in the environment. In addition, the problems do not require a control of the number of robots constructing the formation. In this paper, we first introduce the formation problem in which robots move so that they achieve a desired deployment with the minimum number of robots for a given set of positions of fixed points.

Since the minimum set cover problem with disks in the centralized settings is NP-hard, our goal is to propose approximation algorithms for the minimum SCF problem. First, we show a minimal SCF algorithm from any initial configuration in the asynchronous system. Moreover, we propose an 8-approximation SCF algorithm in the semi-synchronous system for an initial configuration with a low symmetricity. This approximation algorithm achieves 2(1 + 1/l)2 approximation ratio for an initial configuration with the lowest symmetricity (l ≥ 1).

元の言語 | 英語 |
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ホスト出版物のタイトル | Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings |

編集者 | Marcos K. Aguilera, Leonardo Querzoni, Marc Shapiro |

出版者 | Springer Verlag |

ページ | 233-247 |

ページ数 | 15 |

ISBN（電子版） | 9783319144719 |

出版物ステータス | 出版済み - 1 1 2014 |

イベント | 18th International Conference on Principles of Distributed Systems, OPODIS 2014 - Cortina d’Ampezzo, イタリア 継続期間: 12 16 2014 → 12 19 2014 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

巻 | 8878 |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### その他

その他 | 18th International Conference on Principles of Distributed Systems, OPODIS 2014 |
---|---|

国 | イタリア |

市 | Cortina d’Ampezzo |

期間 | 12/16/14 → 12/19/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings*(pp. 233-247). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 8878). Springer Verlag.

**Approximation algorithms for the set cover formation by oblivious mobile robots.** / Izumi, Tomoko; Kamei, Sayaka; Yamauchi, Yukiko.

研究成果: 著書/レポートタイプへの貢献 › 会議での発言

*Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 巻. 8878, Springer Verlag, pp. 233-247, 18th International Conference on Principles of Distributed Systems, OPODIS 2014, Cortina d’Ampezzo, イタリア, 12/16/14.

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AU - Izumi, Tomoko

AU - Kamei, Sayaka

AU - Yamauchi, Yukiko

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Given n robots and n target points on the plane, the minimum set cover formation (SCF) problem requires the robots to form a set cover by the minimum number of robots. In previous formation problems by mobile robots, such as gathering and pattern formation, the problems consist only of the mobile robots, and there are no points fixed in the environment. In addition, the problems do not require a control of the number of robots constructing the formation. In this paper, we first introduce the formation problem in which robots move so that they achieve a desired deployment with the minimum number of robots for a given set of positions of fixed points.Since the minimum set cover problem with disks in the centralized settings is NP-hard, our goal is to propose approximation algorithms for the minimum SCF problem. First, we show a minimal SCF algorithm from any initial configuration in the asynchronous system. Moreover, we propose an 8-approximation SCF algorithm in the semi-synchronous system for an initial configuration with a low symmetricity. This approximation algorithm achieves 2(1 + 1/l)2 approximation ratio for an initial configuration with the lowest symmetricity (l ≥ 1).

AB - Given n robots and n target points on the plane, the minimum set cover formation (SCF) problem requires the robots to form a set cover by the minimum number of robots. In previous formation problems by mobile robots, such as gathering and pattern formation, the problems consist only of the mobile robots, and there are no points fixed in the environment. In addition, the problems do not require a control of the number of robots constructing the formation. In this paper, we first introduce the formation problem in which robots move so that they achieve a desired deployment with the minimum number of robots for a given set of positions of fixed points.Since the minimum set cover problem with disks in the centralized settings is NP-hard, our goal is to propose approximation algorithms for the minimum SCF problem. First, we show a minimal SCF algorithm from any initial configuration in the asynchronous system. Moreover, we propose an 8-approximation SCF algorithm in the semi-synchronous system for an initial configuration with a low symmetricity. This approximation algorithm achieves 2(1 + 1/l)2 approximation ratio for an initial configuration with the lowest symmetricity (l ≥ 1).

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