• Corpus ID: 4901675

Proceedings of the 28th Canadian Conference on Computational Geometry, CCCG 2016, August 3-5, 2016, Simon Fraser University, Vancouver, British Columbia, Canada

@inproceedings{Froese2016ProceedingsOT,
  title={Proceedings of the 28th Canadian Conference on Computational Geometry, CCCG 2016, August 3-5, 2016, Simon Fraser University, Vancouver, British Columbia, Canada},
  author={Vincent Froese and Iyad A. Kanj and Andr{\'e} Nichterlein and Rolf Niedermeier},
  booktitle={Canadian Conference on Computational Geometry},
  year={2016}
}

• Vincent Froese, Iyad A. Kanj, +1 author R. Niedermeier
• Published in
  Canadian Conference on…
  2016
• Computer Science

A fundamental problem in Distributed Computing is the Pattern Formation problem, where some independent mobile entities, called robots, have to rearrange themselves in such a way as to form a given figure from every possible (non-degenerate) initial configuration. In the present paper, we consider robots that operate in the Euclidean plane and are dimensionless, anonymous, oblivious, silent, asynchronous, disoriented, nonchiral, and non-rigid. For this very elementary type of robots, the feasibility of the Pattern Formation problem has been settled, either in the positive or in the negative, for every possible pattern, except for one case: the Square Formation problem by a team of four robots. Here we solve this last case by giving a Square Formation algorithm and proving its correctness. Our contribution represents the concluding chapter in a long thread of research. Our results imply that in the context of the Pattern Formation problem for mobile robots, features such as synchronicity, chirality, and rigidity are computationally irrelevant.