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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
By with high probability, we mean with probability at least \(1-1/n^c\), where n is the number of particles in the system and \(c>0\) is a constant.
We will see this notion of fairness is sufficient to prove the desired runtime for our algorithm; no further assumptions regarding the distribution of the activation sequence are necessary.
If O does contain holes, we consider the subset of particles in each connected region of \(V_\text{eqt}{\setminus } V(O)\) separately.
The logical structure of this section has been significantly updated from its original conference publication in DNA22.
The updated leader election algorithm’s runtime holds with high probability, but its correctness is guaranteed; see Daymude et al. (2017) for details.
References
Angluin D, Aspnes J, Diamadi Z, Fischer MJ, Peralta R (2006) Computation in networks of passively mobile finite-state sensors. Distrib Comput 18(4):235–253
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 135–141
Blázovics L, Lukovszki T, Forstner B (2012b) Target surrounding solution for swarm robots. In: Information and communication technologies (EUNICE ’12), pp 251–262
Bonifaci V, Mehlhorn K, Varma G (2012) Physarum can compute shortest paths. J Theor Biol 309:121–133
Brambilla M, Ferrante E, Birattari M, Dorigo M (2013) Swarm robotics: a review from the swarm engineering perspective. Swarm Intell 7(1):1–41
Chen M, Xin D, Woods D (2015) Parallel computation using active self-assembly. Nat Comput 14(2):225–250
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 117–132
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/1701.03616
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 220–222
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 21:1–21:2
Derakhshandeh Z, Gmyr R, Richa AW, Scheideler C, Strothmann T (2017) Universal coating for programmable matter. Theor Comput Sci 671:56–68
Doty D (2012) Theory of algorithmic self-assembly. Commun ACM 55(12):78–88
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 74–81
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 299–311
Lynch N (1996) Distributed algorithms. Morgan Kauffman, San Francisco
Michail O, Spirakis PG (2016) Simple and efficient local codes for distributed stable network construction. Distrib Comput 29(3):207–237
Patitz MJ (2014) An introduction to tile-based self-assembly and a survey of recent results. Nat Comput 13(2):195–224
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 631–647
Self-organizing particle systems. https://sops.engineering.asu.edu/simulations/
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):303–327
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
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 353–354
Author information
Authors and Affiliations
Corresponding author
Additional information
Joshua J. Daymude, Zahra Derakhshandeh, Alexandra Porter, Andréa W. Richa: Supported in part by NSF Grants CCF-1353089, CCF-1422603, and REU–026935.
Robert Gmyr, Christian Scheideler, Thim Strothmann: Supported in part by DFG Grant SCHE 1592/3-1.
Rights and permissions
About this article
Cite this article
Daymude, J.J., Derakhshandeh, Z., Gmyr, R. et al. On the runtime of universal coating for programmable matter. Nat Comput 17, 81–96 (2018). https://doi.org/10.1007/s11047-017-9658-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-017-9658-6