TY - GEN
T1 - Universal shape formation for programmable matter
AU - Derakhshandeh, Zahra
AU - Gmyr, Robert
AU - Richa, Andrea
AU - Scheideler, Christian
AU - Strothmann, Thim
N1 - Funding Information:
This work was partially supported by the NSF under the Awards CCF-1353089 and CCF-1422603. Furthermore, it was partially supported by DFG grant SCHE 1592/3-1.
Publisher Copyright:
© 2016 ACM.
PY - 2016/7/11
Y1 - 2016/7/11
N2 - We envision programmable matter consisting of systems of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention. Central problems for these particle systems are shape formation and coating problems. In this paper, we present a universal shape formation algorithm which takes an arbitrary shape composed of a constant number of equilateral triangles of unit size and lets the particles build that shape at a scale depending on the number of particles in the system. Our algorithm runs in O(√n) asynchronous execution rounds, where n is the number of particles in the system, provided we start from a well-initialized configuration of the particles. This is optimal in a sense that for any shape deviating from the initial configuration, any movement strategy would require Ω(√n) rounds in the worst case (over all asynchronous activations of the particles). Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
AB - We envision programmable matter consisting of systems of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention. Central problems for these particle systems are shape formation and coating problems. In this paper, we present a universal shape formation algorithm which takes an arbitrary shape composed of a constant number of equilateral triangles of unit size and lets the particles build that shape at a scale depending on the number of particles in the system. Our algorithm runs in O(√n) asynchronous execution rounds, where n is the number of particles in the system, provided we start from a well-initialized configuration of the particles. This is optimal in a sense that for any shape deviating from the initial configuration, any movement strategy would require Ω(√n) rounds in the worst case (over all asynchronous activations of the particles). Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
KW - Distributed algorithms
KW - Programmable matter
KW - Self-Organizing systems
UR - http://www.scopus.com/inward/record.url?scp=84979732902&partnerID=8YFLogxK
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U2 - 10.1145/2935764.2935784
DO - 10.1145/2935764.2935784
M3 - Conference contribution
AN - SCOPUS:84979732902
T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures
SP - 289
EP - 299
BT - SPAA 2016 - Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures
PB - Association for Computing Machinery
T2 - 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016
Y2 - 11 July 2016 through 13 July 2016
ER -