Abstract
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(n2) rounds and moves: this number of moves is also asymptotically optimal.
| Original language | English |
|---|---|
| Title of host publication | 31st International Symposium on Distributed Computing, DISC 2017 |
| Editors | Andrea W. Richa |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959770538 |
| DOIs | |
| Publication status | Published - Oct 1 2017 |
| Event | 31st International Symposium on Distributed Computing, DISC 2017 - Vienna, Austria Duration: Oct 16 2017 → Oct 20 2017 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 91 |
| ISSN (Print) | 1868-8969 |
Other
| Other | 31st International Symposium on Distributed Computing, DISC 2017 |
|---|---|
| Country | Austria |
| City | Vienna |
| Period | 10/16/17 → 10/20/17 |
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All Science Journal Classification (ASJC) codes
- Software
Cite this
Brief announcement : Shape formation by programmable particles. / Di Luna, Giuseppe A.; Flocchini, Paola; Santoro, Nicola; Viglietta, Giovanni; Yamauchi, Yukiko.
31st International Symposium on Distributed Computing, DISC 2017. ed. / Andrea W. Richa. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 91).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Brief announcement
T2 - Shape formation by programmable particles
AU - Di Luna, Giuseppe A.
AU - Flocchini, Paola
AU - Santoro, Nicola
AU - Viglietta, Giovanni
AU - Yamauchi, Yukiko
PY - 2017/10/1
Y1 - 2017/10/1
N2 - 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(n2) rounds and moves: this number of moves is also asymptotically optimal.
AB - 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(n2) rounds and moves: this number of moves is also asymptotically optimal.
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UR - http://www.scopus.com/inward/citedby.url?scp=85032379626&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.DISC.2017.48
DO - 10.4230/LIPIcs.DISC.2017.48
M3 - Conference contribution
AN - SCOPUS:85032379626
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 31st International Symposium on Distributed Computing, DISC 2017
A2 - Richa, Andrea W.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ER -