@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}},
}

@article{33947,
  author       = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
  issn         = {{0304-3975}},
  journal      = {{Theoretical Computer Science}},
  keywords     = {{General Computer Science, Theoretical Computer Science}},
  pages        = {{261--291}},
  publisher    = {{Elsevier BV}},
  title        = {{{Gathering a Euclidean Closed Chain of Robots in Linear Time and Improved Algorithms for Chain-Formation}}},
  doi          = {{10.1016/j.tcs.2022.10.031}},
  volume       = {{939}},
  year         = {{2023}},
}

@inproceedings{34008,
  author       = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Proceedings of the 26th International Conference on Principles of Distributed Systems (OPODIS) }},
  editor       = {{Hillel, Eshcar and Palmieri, Roberto and Riviére, Etienne}},
  isbn         = {{978-3-95977-265-5}},
  issn         = {{1868-8969}},
  location     = {{Brussels}},
  pages        = {{15:1–15:25}},
  publisher    = {{Schloss Dagstuhl – Leibniz Zentrum für Informatik}},
  title        = {{{A Unifying Approach to Efficient (Near-)Gathering of Disoriented Robots with Limited Visibility }}},
  doi          = {{10.4230/LIPIcs.OPODIS.2022.15}},
  volume       = {{253}},
  year         = {{2023}},
}

@inbook{44769,
  author       = {{Castenow, Jannik and Harbig, Jonas and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Lecture Notes in Computer Science}},
  isbn         = {{9783031304477}},
  issn         = {{0302-9743}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Unifying Gathering Protocols for Swarms of Mobile Robots}}},
  doi          = {{10.1007/978-3-031-30448-4_1}},
  year         = {{2023}},
}

@inproceedings{23730,
  author       = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Proceedings of the 17th International Symposium on Algorithms and Experiments for Wireless Sensor Networks (ALGOSENSORS)}},
  editor       = {{Gasieniec, Leszek and Klasing, Ralf and Radzik, Tomasz}},
  location     = {{Lissabon}},
  pages        = {{29 -- 44}},
  publisher    = {{Springer}},
  title        = {{{Gathering a Euclidean Closed Chain of Robots in Linear Time}}},
  doi          = {{10.1007/978-3-030-89240-1_3}},
  volume       = {{12961}},
  year         = {{2021}},
}

@inproceedings{20185,
  author       = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
  booktitle    = {{Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings }},
  editor       = {{Devismes, Stéphane  and  Mittal, Neeraj}},
  isbn         = {{978-3-030-64347-8}},
  pages        = {{60--64}},
  publisher    = {{Springer}},
  title        = {{{Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility }}},
  doi          = {{10.1007/978-3-030-64348-5_5}},
  volume       = {{12514}},
  year         = {{2020}},
}