---
_id: '16449'
abstract:
- lang: eng
text: "We consider the following variant of the two dimensional gathering problem\r\nfor
swarms of robots: Given a swarm of $n$ indistinguishable, point shaped\r\nrobots
on a two dimensional grid. Initially, the robots form a closed chain on\r\nthe
grid and must keep this connectivity during the whole process of their\r\ngathering.
Connectivity means, that neighboring robots of the chain need to be\r\npositioned
at the same or neighboring points of the grid. In our model,\r\ngathering means
to keep shortening the chain until the robots are located\r\ninside a $2\\times
2$ subgrid. Our model is completely local (no global control,\r\nno global coordinates,
no compass, no global communication or vision, \\ldots).\r\nEach robot can only
see its next constant number of left and right neighbors on\r\nthe chain. This
fixed constant is called the \\emph{viewing path length}. All\r\nits operations
and detections are restricted to this constant number of robots.\r\nOther robots,
even if located at neighboring or the same grid point cannot be\r\ndetected. Only
based on the relative positions of its detectable chain\r\nneighbors, a robot
can decide to obtain a certain state. Based on this state\r\nand their local knowledge,
the robots do local modifications to the chain by\r\nmoving to neighboring grid
points without breaking the chain. These\r\nmodifications are performed without
the knowledge whether they lead to a global\r\nprogress or not. We assume the
fully synchronous $\\mathcal{FSYNC}$ model. For\r\nthis problem, we present a
gathering algorithm which needs linear time. This\r\nresult generalizes the result
from \\cite{hopper}, where an open chain with\r\nspecified distinguishable (and
fixed) endpoints is considered."
author:
- first_name: Sebastian
full_name: Abshoff, Sebastian
last_name: Abshoff
- first_name: 'Andreas '
full_name: 'Cord-Landwehr, Andreas '
last_name: Cord-Landwehr
- first_name: Matthias
full_name: Fischer, Matthias
id: '146'
last_name: Fischer
- first_name: Daniel
full_name: Jung, Daniel
id: '37827'
last_name: Jung
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
citation:
ama: Abshoff S, Cord-Landwehr A, Fischer M, Jung D, Meyer auf der Heide F. Gathering
a Closed Chain of Robots on a Grid. *arXiv:151005454*. 2015.
apa: Abshoff, S., Cord-Landwehr, A., Fischer, M., Jung, D., & Meyer auf der
Heide, F. (2015). Gathering a Closed Chain of Robots on a Grid. *ArXiv:1510.05454*.
bibtex: '@article{Abshoff_Cord-Landwehr_Fischer_Jung_Meyer auf der Heide_2015, title={Gathering
a Closed Chain of Robots on a Grid}, journal={arXiv:1510.05454}, author={Abshoff,
Sebastian and Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and
Meyer auf der Heide, Friedhelm}, year={2015} }'
chicago: Abshoff, Sebastian, Andreas Cord-Landwehr, Matthias Fischer, Daniel Jung,
and Friedhelm Meyer auf der Heide. “Gathering a Closed Chain of Robots on a Grid.”
*ArXiv:1510.05454*, 2015.
ieee: S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, and F. Meyer auf der Heide,
“Gathering a Closed Chain of Robots on a Grid,” *arXiv:1510.05454*. 2015.
mla: Abshoff, Sebastian, et al. “Gathering a Closed Chain of Robots on a Grid.”
*ArXiv:1510.05454*, 2015.
short: S. Abshoff, A. Cord-Landwehr, M. Fischer, D. Jung, F. Meyer auf der Heide,
ArXiv:1510.05454 (2015).
date_created: 2020-04-07T07:20:46Z
date_updated: 2022-01-06T06:52:50Z
department:
- _id: '63'
external_id:
arxiv:
- '1510.05454'
language:
- iso: eng
publication: arXiv:1510.05454
status: public
title: Gathering a Closed Chain of Robots on a Grid
type: preprint
user_id: '15415'
year: '2015'
...