A local stochastic algorithm for separation in heterogeneous self-organizing particle systems

Sarah Cannon, Joshua J. Daymude, Cem Gökmen, Dana Randall, Andréa W. Richa

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

Abstract

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.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
EditorsDimitris Achlioptas, Laszlo A. Vegh
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771252
DOIs
StatePublished - Sep 2019
Externally publishedYes
Event22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019 - Cambridge, United States
Duration: Sep 20 2019Sep 22 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume145
ISSN (Print)1868-8969

Conference

Conference22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
CountryUnited States
CityCambridge
Period9/20/199/22/19

Fingerprint

Color
Ising model
Physics
Data storage equipment
Communication
Temperature

Keywords

  • Cluster expansion
  • Markov chains
  • Programmable matter

ASJC Scopus subject areas

  • Software

Cite this

Cannon, S., Daymude, J. J., Gökmen, C., Randall, D., & Richa, A. W. (2019). A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. In D. Achlioptas, & L. A. Vegh (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019 [54] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 145). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.54

A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. / Cannon, Sarah; Daymude, Joshua J.; Gökmen, Cem; Randall, Dana; Richa, Andréa W.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. ed. / Dimitris Achlioptas; Laszlo A. Vegh. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. 54 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 145).

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

Cannon, S, Daymude, JJ, Gökmen, C, Randall, D & Richa, AW 2019, A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. in D Achlioptas & LA Vegh (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019., 54, Leibniz International Proceedings in Informatics, LIPIcs, vol. 145, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019, Cambridge, United States, 9/20/19. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.54
Cannon S, Daymude JJ, Gökmen C, Randall D, Richa AW. A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. In Achlioptas D, Vegh LA, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2019. 54. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.54
Cannon, Sarah ; Daymude, Joshua J. ; Gökmen, Cem ; Randall, Dana ; Richa, Andréa W. / A local stochastic algorithm for separation in heterogeneous self-organizing particle systems. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. editor / Dimitris Achlioptas ; Laszlo A. Vegh. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019. (Leibniz International Proceedings in Informatics, LIPIcs).
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