Shape formation by programmable particles

Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, Yukiko Yamauchi

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

11 引用 (Scopus)


Shape formation (or pattern 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, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (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 (i.e., particles can flip coins to elect a leader). In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S0, SF), allows the particles to form the final shape SF (given in input) starting from the initial shape S0, unknown to the particles. The final configuration will be an appropriate scaled-up copy of SF depending on n. If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles. 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(n2) rounds and moves: this number of moves is also asymptotically worst-case optimal.

ホスト出版物のタイトル21st International Conference on Principles of Distributed Systems, OPODIS 2017
出版者Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
出版物ステータス出版済み - 3 1 2018
イベント21st International Conference on Principles of Distributed Systems, OPODIS 2017 - Lisboa, ポルトガル
継続期間: 12 18 201712 20 2017


その他21st International Conference on Principles of Distributed Systems, OPODIS 2017

All Science Journal Classification (ASJC) codes

  • Software

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  • これを引用

    Di Luna, G. A., Flocchini, P., Santoro, N., Viglietta, G., & Yamauchi, Y. (2018). Shape formation by programmable particles. : 21st International Conference on Principles of Distributed Systems, OPODIS 2017 (巻 95). [31] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.