Advertisement

Natural Computing

, Volume 17, Issue 1, pp 81–96 | Cite as

On the runtime of universal coating for programmable matter

  • Joshua J. Daymude
  • Zahra Derakhshandeh
  • Robert Gmyr
  • Alexandra Porter
  • Andréa W. Richa
  • Christian Scheideler
  • Thim Strothmann
Article

Abstract

Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time. In this paper, we study the problem of uniformly coating objects of arbitrary shape in the context of self-organizing programmable matter, i.e., programmable matter which consists of simple computational elements called particles that can establish and release bonds and can actively move in a self-organized way. Particles are anonymous, have constant-size memory, and utilize only local interactions in order to coat an object. We continue the study of our universal coating algorithm by focusing on its runtime analysis, showing that our algorithm terminates within a linear number of rounds with high probability. We also present a matching linear lower bound that holds with high probability. We use this lower bound to show a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information, which implies that our algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of our algorithm may be better than linear in practice.

Keywords

Distributed algorithms Programmable matter Self-organization Self-organizing systems Coating 

References

  1. Angluin D, Aspnes J, Diamadi Z, Fischer MJ, Peralta R (2006) Computation in networks of passively mobile finite-state sensors. Distrib Comput 18(4):235–253CrossRefzbMATHGoogle Scholar
  2. Blázovics L, Csorba K, Forstner B, Charaf H (2012a) Target tracking and surrounding with swarm robots. In: Proceedings of the 19th IEEE international conference and workshops on the engineering of computer based systems (ECBS ’12), pp 135–141Google Scholar
  3. Blázovics L, Lukovszki T, Forstner B (2012b) Target surrounding solution for swarm robots. In: Information and communication technologies (EUNICE ’12), pp 251–262Google Scholar
  4. Bonifaci V, Mehlhorn K, Varma G (2012) Physarum can compute shortest paths. J Theor Biol 309:121–133MathSciNetCrossRefGoogle Scholar
  5. Brambilla M, Ferrante E, Birattari M, Dorigo M (2013) Swarm robotics: a review from the swarm engineering perspective. Swarm Intell 7(1):1–41CrossRefGoogle Scholar
  6. Chen M, Xin D, Woods D (2015) Parallel computation using active self-assembly. Nat Comput 14(2):225–250MathSciNetCrossRefzbMATHGoogle Scholar
  7. Daymude JJ, Derakhshandeh Z, Gmyr R, Strothmann T, Bazzi RA, Richa AW, Scheideler C (2015) Leader election and shape formation with self-organizing programmable matter. CoRR, abs/1503.07991, 2016. A preliminary version of this work appeared in DNA21, pp 117–132Google Scholar
  8. Daymude JJ, Gmyr R, Richa AW, Scheideler C, Strothmann T (2017) Improved leader election for self-organizing programmable matter. Appeared at the 13th international symposium for algorithms and experiments for wireless networks (ALGOSENSORS ’17). Available at CoRR:abs/1701.03616Google Scholar
  9. Derakhshandeh Z, Dolev S, Gmyr R, Richa AW, Scheideler C, Strothmann T (2014) Brief announcement: amoebot—a new model for programmable matter. In: Proceedings of the 26th ACM symposium on parallelism in algorithms and architectures (SPAA ’14), pp 220–222Google Scholar
  10. Derakhshandeh Z, Gmyr R, Richa AW, Scheideler C, Strothmann T (2015) An algorithmic framework for shape formation problems in self-organizing particle systems. In: Proceedings of the 2nd international conference on nanoscale computing and communication (NanoCom ’15), pp 21:1–21:2Google Scholar
  11. Derakhshandeh Z, Gmyr R, Richa AW, Scheideler C, Strothmann T (2017) Universal coating for programmable matter. Theor Comput Sci 671:56–68MathSciNetCrossRefzbMATHGoogle Scholar
  12. Doty D (2012) Theory of algorithmic self-assembly. Commun ACM 55(12):78–88CrossRefGoogle Scholar
  13. Kumar GP, Berman S (2014) Statistical analysis of stochastic multi-robot boundary coverage. In: Proceedings of the 2014 IEEE international conference on robotics and automation (ICRA ’14), pp 74–81Google Scholar
  14. Li K, Thomas K, Torres C, Rossi L, Shen C-C (2010) Slime mold inspired path formation protocol for wireless sensor networks. In: Proceedings of the 7th international conference on swarm intelligence (ANTS ’10), pp 299–311Google Scholar
  15. Lynch N (1996) Distributed algorithms. Morgan Kauffman, San FranciscozbMATHGoogle Scholar
  16. Michail O, Spirakis PG (2016) Simple and efficient local codes for distributed stable network construction. Distrib Comput 29(3):207–237MathSciNetCrossRefzbMATHGoogle Scholar
  17. Patitz MJ (2014) An introduction to tile-based self-assembly and a survey of recent results. Nat Comput 13(2):195–224MathSciNetCrossRefzbMATHGoogle Scholar
  18. Pavlic TP, Wilson S, Kumar GP, Berman S (2016) An enzyme-inspired approach to stochastic allocation of robotic swarms around boundaries. In: Inaba M, Corke P (eds) Robotics research, Springer tracts in advanced robotics, vol 114. Springer, Cham, pp 631–647Google Scholar
  19. Self-organizing particle systems. https://sops.engineering.asu.edu/simulations/
  20. Wilson S, Pavlic T, Kumar G, Buffin A, Pratt SC, Berman S (2014) Design of ant-inspired stochastic control policies for collective transport by robotic swarms. Swarm Intell 8(4):303–327CrossRefGoogle Scholar
  21. Woods D (2015) Intrinsic universality and the computational power of self-assembly. Philos Trans R Soc A Math Phys Eng Sci.  https://doi.org/10.1098/rsta.2014.0214 Google Scholar
  22. Woods D, Chen H-L, Goodfriend S, Dabby N, Winfree E, Yin P (2013) Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In: Proceedings of the 4th conference on innovations in theoretical computer science (ITCS ’13), pp 353–354Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Joshua J. Daymude
    • 1
  • Zahra Derakhshandeh
    • 1
  • Robert Gmyr
    • 2
  • Alexandra Porter
    • 1
  • Andréa W. Richa
    • 1
  • Christian Scheideler
    • 2
  • Thim Strothmann
    • 2
  1. 1.Computer Science, CIDSEArizona State UniversityTempeUSA
  2. 2.Department of Computer SciencePaderborn UniversityPaderbornGermany

Personalised recommendations