### 抜粋

Shape formation is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane, have constant memory, can only communicate with neighboring particles, and can only move from a grid node to an empty neighboring node; their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization. In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. As a byproduct, if randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that n is large enough. Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential. We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n^{2}) rounds and moves: this number of moves is also asymptotically optimal.

元の言語 | 英語 |
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ホスト出版物のタイトル | 31st International Symposium on Distributed Computing, DISC 2017 |

編集者 | Andrea W. Richa |

出版者 | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN（電子版） | 9783959770538 |

DOI | |

出版物ステータス | 出版済み - 10 1 2017 |

イベント | 31st International Symposium on Distributed Computing, DISC 2017 - Vienna, オーストリア 継続期間: 10 16 2017 → 10 20 2017 |

### 出版物シリーズ

名前 | Leibniz International Proceedings in Informatics, LIPIcs |
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巻 | 91 |

ISSN（印刷物） | 1868-8969 |

### その他

その他 | 31st International Symposium on Distributed Computing, DISC 2017 |
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国 | オーストリア |

市 | Vienna |

期間 | 10/16/17 → 10/20/17 |

### All Science Journal Classification (ASJC) codes

- Software

## フィンガープリント Brief announcement: Shape formation by programmable particles' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*31st International Symposium on Distributed Computing, DISC 2017*(Leibniz International Proceedings in Informatics, LIPIcs; 巻数 91). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.DISC.2017.48