Brief announcement: Shape formation by programmable particles

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish
Title of host publication31st International Symposium on Distributed Computing, DISC 2017
EditorsAndrea W. Richa
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770538
DOIs
Publication statusPublished - Oct 1 2017
Event31st International Symposium on Distributed Computing, DISC 2017 - Vienna, Austria
Duration: Oct 16 2017Oct 20 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume91
ISSN (Print)1868-8969

Other

Other31st International Symposium on Distributed Computing, DISC 2017
CountryAustria
CityVienna
Period10/16/1710/20/17

Fingerprint

Chirality
Chemical activation
Mobile robots
Byproducts
Data storage equipment

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Di Luna, G. A., Flocchini, P., Santoro, N., Viglietta, G., & Yamauchi, Y. (2017). Brief announcement: Shape formation by programmable particles. In A. W. Richa (Ed.), 31st International Symposium on Distributed Computing, DISC 2017 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 91). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.DISC.2017.48

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 proceedingConference contribution

Di Luna, GA, Flocchini, P, Santoro, N, Viglietta, G & Yamauchi, Y 2017, Brief announcement: Shape formation by programmable particles. in AW Richa (ed.), 31st International Symposium on Distributed Computing, DISC 2017. Leibniz International Proceedings in Informatics, LIPIcs, vol. 91, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 31st International Symposium on Distributed Computing, DISC 2017, Vienna, Austria, 10/16/17. https://doi.org/10.4230/LIPIcs.DISC.2017.48
Di Luna GA, Flocchini P, Santoro N, Viglietta G, Yamauchi Y. Brief announcement: Shape formation by programmable particles. In Richa AW, editor, 31st International Symposium on Distributed Computing, DISC 2017. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2017. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.DISC.2017.48
Di Luna, Giuseppe A. ; Flocchini, Paola ; Santoro, Nicola ; Viglietta, Giovanni ; Yamauchi, Yukiko. / Brief announcement : Shape formation by programmable particles. 31st International Symposium on Distributed Computing, DISC 2017. editor / Andrea W. Richa. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs).
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