Gathering a Closed Chain of Robots on a Grid

S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, F. Meyer auf der Heide, in: Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS), IEEE, 2016, pp. 689–699.

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We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of n indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid and must keep this connectivity during the whole process of their gathering. Connectivity means, that neighboring robots of the chain need to be positioned at the same or neighboring points of the grid. In our model, gathering means to keep shortening the chain until the robots are located inside a 2*2 subgrid. Our model is completely local (no global control, no global coordinates, no compass, no global communication or vision, ...). Each robot can only see its next constant number of left and right neighbors on the chain. This fixed constant is called the viewing path length. All its operations and detections are restricted to this constant number of robots. Other robots, even if located at neighboring or the same grid point cannot be detected. Only based on the relative positions of its detectable chain neighbors, a robot can decide to obtain a certain state. Based on this state and their local knowledge, the robots do local modifications to the chain by moving to neighboring grid points without breaking the chain. These modifications are performed without the knowledge whether they lead to a global progress or not. We assume the fully synchronous FSYNC model. For this problem, we present a gathering algorithm which needs linear time. This result generalizes a result, where an open chain with specified distinguishable (and fixed) endpoints is considered.
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Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS)
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689-699
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Abshoff S, Cord-Landwehr A, Fischer M, Jung D, Meyer auf der Heide F. Gathering a Closed Chain of Robots on a Grid. In: Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS). IEEE; 2016:689-699. doi:10.1109/IPDPS.2016.51
Abshoff, S., Cord-Landwehr, A., Fischer, M., Jung, D., & Meyer auf der Heide, F. (2016). Gathering a Closed Chain of Robots on a Grid. In Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS) (pp. 689–699). IEEE. https://doi.org/10.1109/IPDPS.2016.51
@inproceedings{Abshoff_Cord-Landwehr_Fischer_Jung_Meyer auf der Heide_2016, title={Gathering a Closed Chain of Robots on a Grid}, DOI={10.1109/IPDPS.2016.51}, booktitle={Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS)}, publisher={IEEE}, author={Abshoff, Sebastian and Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}, year={2016}, pages={689–699} }
Abshoff, Sebastian, Andreas Cord-Landwehr, Matthias Fischer, Daniel Jung, and Friedhelm Meyer auf der Heide. “Gathering a Closed Chain of Robots on a Grid.” In Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS), 689–99. IEEE, 2016. https://doi.org/10.1109/IPDPS.2016.51.
S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, and F. Meyer auf der Heide, “Gathering a Closed Chain of Robots on a Grid,” in Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS), 2016, pp. 689–699.
Abshoff, Sebastian, et al. “Gathering a Closed Chain of Robots on a Grid.” Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS), IEEE, 2016, pp. 689–99, doi:10.1109/IPDPS.2016.51.

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