Abstract
We consider programmable matter that consists of computationally limited devices (called particles) that are able to self-organize in order to achieve some collective goal without the need for central control or external intervention. We use the geometric amoebot model to describe such self-organizing particle systems, which defines how particles can actively move and communicate with one another. In this paper, we present an efficient local-control algorithm which solves the leader election problem in \(\mathcal {O}(n)\) asynchronous rounds with high probability, where n is the number of particles in the system. Our algorithm relies only on local information — particles do not have unique identifiers, any knowledge of n, or any sort of global coordinate system — and requires only constant memory per particle.
J. J. Daymude and A. W. Richa—Supported in part by NSF awards CCF-1422603 and CCF-1637393.
R. Gmyr, C. Scheideler and T. Strothmann—Supported in part by DFG grant SCHE 1592/3-1.
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Notes
- 1.
An event occurs with high probability (w.h.p.), if the probability of success is at least \(1 - n^{-c}\), where \(c > 1\) is a constant; in our context, n is the number of particles.
- 2.
An astute reader may note that a w.h.p. guarantee on correctness is weaker than the absolute guarantee given for the algorithm in [14], but the latter was given without considering the necessary particle-level execution details.
- 3.
This w.h.p. guarantee results from there being a small but nonzero probability that either (a) all agents flip tails and become non-candidates in the segment setup phase, or (b) more than one candidate generates the same highest identifier in the identifier setup phase. See [9] for more details.
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Daymude, J.J., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T. (2017). Improved Leader Election for Self-organizing Programmable Matter. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M., Zhang, Y. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2017. Lecture Notes in Computer Science(), vol 10718. Springer, Cham. https://doi.org/10.1007/978-3-319-72751-6_10
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