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International Conference on DNA-Based Computers

DNA 2017: DNA Computing and Molecular Programming pp 122–138Cite as

A Stochastic Approach to Shortcut Bridging in Programmable Matter

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10467))

Abstract

In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider stochastic, distributed, local, asynchronous algorithms for “shortcut bridging,” in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eticon have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency tradeoff using local interactions [1]. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being “shortcut” similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. The proposed algorithm demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple generalization of a stochastic algorithm for compression [2].

S. Cannon—Supported in part by NSF DGE-1148903 and a grant from the Simons Foundation (#361047).

J.J. Daymude—Supported in part by NSF CCF-1637393.

D. Randall—Supported in part by NSF CCF-1637031 and CCF-1526900.

A.W. Richa—Supported in part by NSF CCF-1637393 and CCF-1422603.

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Notes

  1. 1.

    The notion of a particle (resp., location) neighborhood N(P) (resp., \(N(\ell )\)) has been extended from [2] to include objects.

  2. 2.

    Since particles treat objects as static particles, the particle system may actually disconnect into several components which remain connected through objects.

  3. 3.

    If \(\sigma _0\) has holes, our algorithm will eliminate them and they will not reform [2]; for simplicity, we focus only on the behavior of the system after this occurs.

  4. 4.

    Note only a constant number of bits are needed to produce q, as \(\lambda \) and \(\gamma \) are constants and a particle move changes perimeter and gap perimeter by at most a constant.

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Author information

Authors and Affiliations

  1. University of Granada, Granada, Spain

    Marta Andrés Arroyo

  2. College of Computing, Georgia Institute of Technology, Atlanta, USA

    Sarah Cannon & Dana Randall

  3. Computer Science, CIDSE, Arizona State University, Tempe, USA

    Joshua J. Daymude & Andréa W. Richa

Authors
  1. Marta Andrés Arroyo
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  2. Sarah Cannon
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  3. Joshua J. Daymude
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  4. Dana Randall
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  5. Andréa W. Richa
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Correspondence to Sarah Cannon .

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Editors and Affiliations

  1. Hasselt University, Diepenbeek, Belgium

    Robert Brijder

  2. California Institute of Technology, Pasadena, California, USA

    Lulu Qian

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Andrés Arroyo, M., Cannon, S., Daymude, J.J., Randall, D., Richa, A.W. (2017). A Stochastic Approach to Shortcut Bridging in Programmable Matter. In: Brijder, R., Qian, L. (eds) DNA Computing and Molecular Programming. DNA 2017. Lecture Notes in Computer Science(), vol 10467. Springer, Cham. https://doi.org/10.1007/978-3-319-66799-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-66799-7_9

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