TY - GEN
T1 - A local stochastic algorithm for separation in heterogeneous self-organizing particle systems
AU - Cannon, Sarah
AU - Daymude, Joshua J.
AU - Gökmen, Cem
AU - Randall, Dana
AU - Richa, Andréa W.
N1 - Funding Information:
Funding Sarah Cannon: Supported by National Science Foundation (NSF) award DMS-1803325. Joshua J. Daymude: Supported by NSF awards CCF-1422603, CCF-1637393, and CCF-1733680. Cem Gökmen: Supported by NSF award CCF-1733812. Dana Randall: Supported by NSF awards CCF-1526900, CCF-1637031, and CCF-1733812. Andréa W. Richa: Supported by NSF awards CCF-1422603, CCF-1637393, and CCF-1733680.
Publisher Copyright:
© Sarah Cannon, Joshua J. Daymude, Cem Gökmen, Dana Randall, and Andréa W. Richa.
PY - 2019/9
Y1 - 2019/9
N2 - We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC’16) that can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM’11), the high-temperature expansion of the Ising model, and careful probabilistic arguments.
AB - We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC’16) that can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM’11), the high-temperature expansion of the Ising model, and careful probabilistic arguments.
KW - Cluster expansion
KW - Markov chains
KW - Programmable matter
UR - http://www.scopus.com/inward/record.url?scp=85072865042&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072865042&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2019.54
DO - 10.4230/LIPIcs.APPROX-RANDOM.2019.54
M3 - Conference contribution
AN - SCOPUS:85072865042
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
A2 - Achlioptas, Dimitris
A2 - Vegh, Laszlo A.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Y2 - 20 September 2019 through 22 September 2019
ER -