### Abstract

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).

Original language | English |
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Title of host publication | Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings |

Editors | Marcos K. Aguilera, Leonardo Querzoni, Marc Shapiro |

Publisher | Springer Verlag |

Pages | 233-247 |

Number of pages | 15 |

ISBN (Electronic) | 9783319144719 |

Publication status | Published - Jan 1 2014 |

Event | 18th International Conference on Principles of Distributed Systems, OPODIS 2014 - Cortina d’Ampezzo, Italy Duration: Dec 16 2014 → Dec 19 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8878 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th International Conference on Principles of Distributed Systems, OPODIS 2014 |
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Country | Italy |

City | Cortina d’Ampezzo |

Period | 12/16/14 → 12/19/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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); Vol. 8878). Springer Verlag.

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

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

*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), vol. 8878, Springer Verlag, pp. 233-247, 18th International Conference on Principles of Distributed Systems, OPODIS 2014, Cortina d’Ampezzo, Italy, 12/16/14.

}

TY - GEN

T1 - Approximation algorithms for the set cover formation by oblivious mobile robots

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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M3 - Conference contribution

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 233

EP - 247

BT - Principles of Distributed Systems - 18th International Conference, OPODIS 2014, Proceedings

A2 - Aguilera, Marcos K.

A2 - Querzoni, Leonardo

A2 - Shapiro, Marc

PB - Springer Verlag

ER -