---
_id: '66838'
abstract:
- lang: eng
  text: 'The sliding square model is a widely used abstraction for studying self-reconfigurable
    robotic systems, where modules are square-shaped robots that move by sliding or
    rotating over one another. In this paper, we propose a novel distributed algorithm
    that enables a group of modules to reconfigure into a rhombus shape, starting
    from an arbitrary side-connected configuration. It is connectivity-preserving
    and operates under minimal assumptions: one leader module, common chirality, constant
    memory per module, and visibility and communication restricted to immediate neighbors.
    Unlike prior work, which relaxes the original sliding square move-set, our approach
    uses the unmodified move-set, addressing the additional challenge of handling
    locked configurations. Our algorithm is sequential in nature and operates with
    a worst-case time complexity of O(n^2) rounds, which is optimal for sequential
    algorithms. To improve runtime, we introduce two parallel variants of the algorithm.
    Both rely on a spanning tree data structure, allowing modules to make decisions
    based on local connectivity. Our experimental results show a significant speedup
    for the first variant, and a linear average runtime for the second variant, which
    is worst-case optimal for parallel algorithms.'
article_number: '116196'
article_type: original
author:
- first_name: Irina
  full_name: Kostitsyna, Irina
  last_name: Kostitsyna
- first_name: David
  full_name: Liedtke, David
  id: '55557'
  last_name: Liedtke
- first_name: Christian
  full_name: Scheideler, Christian
  id: '20792'
  last_name: Scheideler
citation:
  ama: Kostitsyna I, Liedtke D, Scheideler C. Distributed rhombus formation of sliding
    squares. <i>Theoretical Computer Science</i>. 2026;1085. doi:<a href="https://doi.org/10.1016/j.tcs.2026.116196">10.1016/j.tcs.2026.116196</a>
  apa: Kostitsyna, I., Liedtke, D., &#38; Scheideler, C. (2026). Distributed rhombus
    formation of sliding squares. <i>Theoretical Computer Science</i>, <i>1085</i>,
    Article 116196. <a href="https://doi.org/10.1016/j.tcs.2026.116196">https://doi.org/10.1016/j.tcs.2026.116196</a>
  bibtex: '@article{Kostitsyna_Liedtke_Scheideler_2026, title={Distributed rhombus
    formation of sliding squares}, volume={1085}, DOI={<a href="https://doi.org/10.1016/j.tcs.2026.116196">10.1016/j.tcs.2026.116196</a>},
    number={116196}, journal={Theoretical Computer Science}, publisher={Elsevier BV},
    author={Kostitsyna, Irina and Liedtke, David and Scheideler, Christian}, year={2026}
    }'
  chicago: Kostitsyna, Irina, David Liedtke, and Christian Scheideler. “Distributed
    Rhombus Formation of Sliding Squares.” <i>Theoretical Computer Science</i> 1085
    (2026). <a href="https://doi.org/10.1016/j.tcs.2026.116196">https://doi.org/10.1016/j.tcs.2026.116196</a>.
  ieee: 'I. Kostitsyna, D. Liedtke, and C. Scheideler, “Distributed rhombus formation
    of sliding squares,” <i>Theoretical Computer Science</i>, vol. 1085, Art. no.
    116196, 2026, doi: <a href="https://doi.org/10.1016/j.tcs.2026.116196">10.1016/j.tcs.2026.116196</a>.'
  mla: Kostitsyna, Irina, et al. “Distributed Rhombus Formation of Sliding Squares.”
    <i>Theoretical Computer Science</i>, vol. 1085, 116196, Elsevier BV, 2026, doi:<a
    href="https://doi.org/10.1016/j.tcs.2026.116196">10.1016/j.tcs.2026.116196</a>.
  short: I. Kostitsyna, D. Liedtke, C. Scheideler, Theoretical Computer Science 1085
    (2026).
date_created: 2026-08-25T05:30:39Z
date_updated: 2026-08-25T05:37:47Z
department:
- _id: '34'
- _id: '7'
- _id: '79'
doi: 10.1016/j.tcs.2026.116196
intvolume: '      1085'
keyword:
- modular robots
- distributed algorithms
- sliding squares
language:
- iso: eng
publication: Theoretical Computer Science
publication_identifier:
  issn:
  - 0304-3975
publication_status: published
publisher: Elsevier BV
status: public
title: Distributed rhombus formation of sliding squares
type: journal_article
user_id: '55557'
volume: 1085
year: '2026'
...
---
_id: '22510'
abstract:
- lang: eng
  text: 'Over the past decades, the Gathering problem, which asks to gather a group
    of robots in finite time given some restrictions, has been intensively studied.
    In this paper, we are given a group of n autonomous, dimensionless, deterministic,
    and anonymous robots, with bounded viewing range. Assuming a continuous time model,
    the goal is to gather these robots into one point in finite time. We introduce
    a simple convergence criterion that defines a new class of algorithms which perform
    gathering in O(nd) time, where d is the diameter of the initial robot configuration.
    We show that some gathering algorithms in the literature belong to this class
    and propose two new algorithms that belong to this class and have quadratic running
    time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center
    algorithm (S-GTRC). We prove that the latter can perform gathering without collision
    by using a slightly more complex robot model: non oblivious, chiral, and luminous
    (i.e. robots have observable external memory, as in [8]). We also consider a variant
    of the Gathering problem, the Near-Gathering problem, in which robots must get
    close to each other without colliding. We show that S-GTRC solves the Near-Gathering
    problem in quadratic time and assumes a weaker robot model than the one assumed
    in the current state-of-the-art.'
author:
- first_name: Shouwei
  full_name: Li, Shouwei
  last_name: Li
- first_name: Christine
  full_name: Markarian, Christine
  last_name: Markarian
- first_name: Friedhelm
  full_name: Meyer auf der Heide, Friedhelm
  id: '15523'
  last_name: Meyer auf der Heide
- first_name: Pavel
  full_name: Podlipyan, Pavel
  last_name: Podlipyan
citation:
  ama: Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. A continuous strategy
    for collisionless gathering. <i>Theoretical Computer Science</i>. 2021;852:41-60.
    doi:<a href="https://doi.org/10.1016/j.tcs.2020.10.037">10.1016/j.tcs.2020.10.037</a>
  apa: Li, S., Markarian, C., Meyer auf der Heide, F., &#38; Podlipyan, P. (2021).
    A continuous strategy for collisionless gathering. <i>Theoretical Computer Science</i>,
    <i>852</i>, 41–60. <a href="https://doi.org/10.1016/j.tcs.2020.10.037">https://doi.org/10.1016/j.tcs.2020.10.037</a>
  bibtex: '@article{Li_Markarian_Meyer auf der Heide_Podlipyan_2021, title={A continuous
    strategy for collisionless gathering}, volume={852}, DOI={<a href="https://doi.org/10.1016/j.tcs.2020.10.037">10.1016/j.tcs.2020.10.037</a>},
    journal={Theoretical Computer Science}, author={Li, Shouwei and Markarian, Christine
    and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={41–60}
    }'
  chicago: 'Li, Shouwei, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel
    Podlipyan. “A Continuous Strategy for Collisionless Gathering.” <i>Theoretical
    Computer Science</i> 852 (2021): 41–60. <a href="https://doi.org/10.1016/j.tcs.2020.10.037">https://doi.org/10.1016/j.tcs.2020.10.037</a>.'
  ieee: S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “A continuous
    strategy for collisionless gathering,” <i>Theoretical Computer Science</i>, vol.
    852, pp. 41–60, 2021.
  mla: Li, Shouwei, et al. “A Continuous Strategy for Collisionless Gathering.” <i>Theoretical
    Computer Science</i>, vol. 852, 2021, pp. 41–60, doi:<a href="https://doi.org/10.1016/j.tcs.2020.10.037">10.1016/j.tcs.2020.10.037</a>.
  short: S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer
    Science 852 (2021) 41–60.
date_created: 2021-06-28T09:24:15Z
date_updated: 2022-01-06T06:55:35Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.10.037
intvolume: '       852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 41-60
publication: Theoretical Computer Science
publication_identifier:
  issn:
  - 0304-3975
publication_status: published
status: public
title: A continuous strategy for collisionless gathering
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...
---
_id: '22511'
abstract:
- lang: eng
  text: "In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center
    algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile
    robots with limited viewing range in the plane. Remarquably, this algorithm exploits
    the fact that during its execution, many collisions of robots occur. Such collisions
    are interpreted as a success because it is assumed that such collided robots behave
    the same from now on. This is acceptable under the assumption that each robot
    is represented by a single point. Otherwise, collisions should be avoided. In
    this paper, we consider a continuous Go-To-The-Center algorithm in which the robots
    continuously observe the positions of their neighbors and adapt their speed (assuming
    a speed limit) and direction. Our first results are time bounds of O(n2) for gathering
    in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution
    is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center
    considering only the neighbors of a robot with respect to the Gabriel subgraph
    of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that
    this modification still correctly executes gathering in one and two dimensions,
    with the same time bounds as above. Simulations exhibit a severe difference of
    the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms:
    Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm,
    typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center
    algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center
    algorithm for one dimension. In two-dimensional Euclidean space, we conjecture
    that the “collisionless property” holds for almost every initial configuration.
    We support our conjecture with measurements obtained from the simulation where
    robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms.\r\n"
author:
- first_name: Shouwei
  full_name: Li, Shouwei
  last_name: Li
- first_name: Friedhelm
  full_name: Meyer auf der Heide, Friedhelm
  id: '15523'
  last_name: Meyer auf der Heide
- first_name: Pavel
  full_name: Podlipyan, Pavel
  last_name: Podlipyan
citation:
  ama: Li S, Meyer auf der Heide F, Podlipyan P. The impact of the Gabriel subgraph
    of the visibility graph on the gathering of mobile autonomous robots. <i>Theoretical
    Computer Science</i>. 2021;852:29-40. doi:<a href="https://doi.org/10.1016/j.tcs.2020.11.009">10.1016/j.tcs.2020.11.009</a>
  apa: Li, S., Meyer auf der Heide, F., &#38; Podlipyan, P. (2021). The impact of
    the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
    robots. <i>Theoretical Computer Science</i>, <i>852</i>, 29–40. <a href="https://doi.org/10.1016/j.tcs.2020.11.009">https://doi.org/10.1016/j.tcs.2020.11.009</a>
  bibtex: '@article{Li_Meyer auf der Heide_Podlipyan_2021, title={The impact of the
    Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
    robots}, volume={852}, DOI={<a href="https://doi.org/10.1016/j.tcs.2020.11.009">10.1016/j.tcs.2020.11.009</a>},
    journal={Theoretical Computer Science}, author={Li, Shouwei and Meyer auf der
    Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={29–40} }'
  chicago: 'Li, Shouwei, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The
    Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile
    Autonomous Robots.” <i>Theoretical Computer Science</i> 852 (2021): 29–40. <a
    href="https://doi.org/10.1016/j.tcs.2020.11.009">https://doi.org/10.1016/j.tcs.2020.11.009</a>.'
  ieee: S. Li, F. Meyer auf der Heide, and P. Podlipyan, “The impact of the Gabriel
    subgraph of the visibility graph on the gathering of mobile autonomous robots,”
    <i>Theoretical Computer Science</i>, vol. 852, pp. 29–40, 2021.
  mla: Li, Shouwei, et al. “The Impact of the Gabriel Subgraph of the Visibility Graph
    on the Gathering of Mobile Autonomous Robots.” <i>Theoretical Computer Science</i>,
    vol. 852, 2021, pp. 29–40, doi:<a href="https://doi.org/10.1016/j.tcs.2020.11.009">10.1016/j.tcs.2020.11.009</a>.
  short: S. Li, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science
    852 (2021) 29–40.
date_created: 2021-06-28T09:34:45Z
date_updated: 2022-01-06T06:55:35Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.11.009
intvolume: '       852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 29-40
publication: Theoretical Computer Science
publication_identifier:
  issn:
  - 0304-3975
publication_status: published
status: public
title: The impact of the Gabriel subgraph of the visibility graph on the gathering
  of mobile autonomous robots
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...