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Computing by Programmable Particles

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Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

The vision for programmable matter is to realize a physical substance that is scalable, versatile, instantly reconfigurable, safe to handle, and robust to failures. Programmable matter could be deployed in a variety of domain spaces to address a wide gamut of problems, including applications in construction, environmental science, synthetic biology, and space exploration. However, there are considerable engineering and computational challenges that must be overcome before such a system could be implemented. Towards developing efficient algorithms for novel programmable matter behaviors, the amoebot model for self-organizing particle systems and its variant, hybrid programmable matter, provide formal computational frameworks that facilitate rigorous algorithmic research. In this chapter, we discuss distributed algorithms under these models for shape formation, shape recognition, object coating, compression, shortcut bridging, and separation in addition to some underlying algorithmic primitives.

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Notes

  1. 1.

    Some papers refer to \(G_{\varDelta }\) as the equilateral triangular grid graph \(G_\text {eqt}\) or the triangular lattice \(\varGamma \).

  2. 2.

    A particle can only write into its own memory in the amoebot model’s publishing-based communication, so no conflicts of concurrent writes to the same memory location are possible.

  3. 3.

    An event occurs with high probability (w.h.p.) if the probability of success is at least \(1 - 1 / n^c\), where \(c > 0\) is a constant; in our setting, n is the number of particles.

  4. 4.

    In [16], the digits are chosen uniformly at random from \([0, r-1]\) where r is a fixed constant. The resulting identifiers are numbers with radix r.

  5. 5.

    For this presentation, we use a simplified scheme that results in a triangle with the seed at its center; the original scheme given in [19, 52] is significantly more complex and results in a triangle with the seed at one vertex.

  6. 6.

    The original publication on “universal” shape formation [20] claimed the algorithm could construct any shape with a constant number of faces. However, Gmyr corrected an oversight in this paper’s analysis in his Ph.D. thesis [29] and, as a result, the class of shapes had to be restricted to sequentially constructible shapes.

  7. 7.

    This definition of configuration connectivity is equivalent to that of system connectivity given in Sect. 2.2.

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Acknowledgements

Our warmest gratitude belongs to all of our wonderful collaborators, both past and present, without whom this research would not have been possible. We would like to thank Robert Gmyr, Thim Strothmann, and Zahra Derakhshandeh for their trailblazing work on self-organizing particle systems during their Ph.D. studies. We would especially like to thank Robert for letting us use materials from his Ph.D. thesis for this chapter (in particular, his excellent images). To Dana Randall and Sarah Cannon, thank you for leading us into a new paradigm by showing us just how much one can do with a whole lot of randomness. To Irina Kostitsyna and Dorian Rudolph, thank you for all your work in developing hybrid programmable matter. Finally, to our undergraduate research assistants, especially Alexandra Porter: thank you for your enthusiasm, energy, and effort.

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Daymude, J.J., Hinnenthal, K., Richa, A.W., Scheideler, C. (2019). Computing by Programmable Particles. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_22

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