Abstract
In the geometric Amoebot model, programmable matter is viewed as a very large number of identical micro/nano-sized entities, called particles, operating on a hexagonal tessellation of the plane, with limited computational capabilities, interacting only with neighboring particles, and moving from a grid node to an empty neighboring node. An important requirement, common to most research in this model, is that the particles must be connected at all times.
Within this model, a central concern has been the formation of geometric shapes; in particular, the line is the elementary shape used as the basis to form more complex shapes, and as a step to solve complex tasks. If some of the particles on the line are faulty it might be necessary for the non-faulty particles to reconstruct a line that does not contain faulty particles. In this paper we study the Connected Line Recovery problem of reconstructing the line without violating the connectivity requirement. We provide a complete feasibility characterization of the problem, identifying the conditions necessary for its solvability, and constructively proving the sufficiency of those conditions. Our algorithm allows the non-faulty particles to solve the problem, regardless of the initial distribution of the faults and of their number.
Supported in part by NSERC under the Discovery Grant program.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cannon, S., Daymude, J., Randall, D., Richa, A.: A Markov chain algorithm for compression in self-organizing particle systems. In: Proceedings of 35th Symposium on Principles of Distributed Computing (PODC), pp. 279–288 (2016)
Chirikjian, G.: Kinematics of a metamorphic robotic system. In: Proceedings of the International Conference on Robotics and Automation, pp. 1:449–1:455 (1994)
Daymude, J.J., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Improved leader election for self-organizing programmable matter. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 127–140. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_10
Daymude, J., Hinnenthal, K., Richa, A., Scheideler, C.: Computing by programmable particles. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, pp. 615–681. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_22
Derakhshandeh, Z., Gmyr, R., Richa, A., Scheideler, C., Strothmann, T.: An algorithmic framework for shape formation problems in self-organizing particle systems. In: Proceedings of NanoCom, pp. 21:1–21:2 (2015)
Derakhshandeh, Z., Gmyr, R., Richa, A., Scheideler, C., Strothmann, T.: Universal shape formation for programmable matter. In: Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 289–299 (2016)
Derakhshandeh, Z., Gmyr, R., Richa, A., Scheideler, C., Strothmann, T.: Universal coating for programmable matter. Theoret. Comput. Sci. 671, 56–68 (2017)
Derakhshandeh, Z., Gmyr, R., Strothmann, T., Bazzi, R., Richa, A.W., Scheideler, C.: Leader election and shape formation with self-organizing programmable matter. In: Phillips, A., Yin, P. (eds.) DNA 2015. LNCS, vol. 9211, pp. 117–132. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21999-8_8
Derakhshandeh, Z., Dolev, S., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Brief announcement: Amoebot - a new model for programmable matter. In: Proceedings of 26th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 220-222 (2014)
Di Luna, G., Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Line recovery by programmable particles. In: Proceedings of the International Conference on Distributed Computing and Networking (ICDCN), pp. 4.1–4.10 (2018)
Di Luna, G.A., Flocchini, P., Santoro, N., Viglietta, G., Yamauchi, Y.: Shape formation by programmable particles. Distrib. Comput. 33(1), 69–101 (2019). https://doi.org/10.1007/s00446-019-00350-6
Di Luna, G.A., Flocchini, P., Santoro, N., Viglietta, G., Yamauchi, Y.: Mobile RAM and shape formation by programmable particles. In: Malawski, M., Rzadca, K. (eds.) Euro-Par 2020. LNCS, vol. 12247, pp. 343–358. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57675-2_22
Dolev, S., Frenkel, S., Rosenbli, M., Narayanan, P., Venkateswarlu, K.: In-vivo energy harvesting nano robots. In: Proceedings of ICSEE, pp. 1–5 (2016)
Patitz, M.J.: An introduction to tile-based self-assembly and a survey of recent results. Natural Comput. 13(2), 195–224 (2013). https://doi.org/10.1007/s11047-013-9379-4
Rothemund, P.: Folding DNA to create nanoscale shapes and patterns. Nature 440(7082), 297–302 (2006)
Walter, J., Welch, J., Amato, N.: Distributed reconfiguration of metamorphic robot chains. Distrib. Comput. 17(2), 171–189 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Nokhanji, N., Santoro, N. (2020). Line Reconfiguration by Programmable Particles Maintaining Connectivity. In: Martín-Vide, C., Vega-Rodríguez, M.A., Yang, MS. (eds) Theory and Practice of Natural Computing. TPNC 2020. Lecture Notes in Computer Science(), vol 12494. Springer, Cham. https://doi.org/10.1007/978-3-030-63000-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-63000-3_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-62999-1
Online ISBN: 978-3-030-63000-3
eBook Packages: Computer ScienceComputer Science (R0)