@inproceedings{56298,
  abstract     = {{In the general pattern formation (GPF) problem, a swarm of simple autonomous,
disoriented robots must form a given pattern. The robots' simplicity imply a
strong limitation: When the initial configuration is rotationally symmetric,
only patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS
2010]. The only known algorithm to form large patterns with limited visibility
and without memory requires the robots to start in a near-gathering (a swarm of
constant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know
any near-gathering algorithm guaranteed to preserve symmetry but most natural
gathering strategies trivially increase symmetries [Castenow et al.; OPODIS
2022].
  Thus, we study near-gathering without changing the swarm's rotational
symmetry for disoriented, oblivious robots with limited visibility (the
OBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on
the theory of dynamical systems to analyze how a given algorithm affects
symmetry and provide sufficient conditions for symmetry preservation. Until
now, it was unknown whether the considered OBLOT-model allows for any
non-trivial algorithm that always preserves symmetry. Our first result shows
that a variant of Go-to-the-Average always preserves symmetry but may sometimes
lead to multiple, unconnected near-gathering clusters. Our second result is a
symmetry-preserving near-gathering algorithm that works on swarms with a convex
boundary (the outer boundary of the unit disc graph) and without holes (circles
of diameter 1 inside the boundary without any robots).}},
  author       = {{Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter}},
  booktitle    = {{28th International Conference on Principles of Distributed Systems (OPODIS 2024)}},
  editor       = {{Bonomi, Silvia and Galletta, Letterio and Rivière,  Etienne and Schiavoni,  Valerio}},
  isbn         = {{978-3-95977-360-7}},
  issn         = {{1868-8969}},
  keywords     = {{Swarm Algorithm, Swarm Robots, Distributed Algorithm, Pattern Formation, Limited Visibility, Oblivious}},
  location     = {{Lucca, Italy}},
  publisher    = {{Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}},
  title        = {{{Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility}}},
  doi          = {{10.4230/LIPIcs.OPODIS.2024.13}},
  volume       = {{324}},
  year         = {{2025}},
}