---
_id: '17811'
abstract:
- lang: eng
text: "We consider a swarm of $n$ autonomous mobile robots, distributed on a\r\n2-dimensional
grid. A basic task for such a swarm is the gathering process: All\r\nrobots have
to gather at one (not predefined) place. A common local model for\r\nextremely
simple robots is the following: The robots do not have a common\r\ncompass, only
have a constant viewing radius, are autonomous and\r\nindistinguishable, can move
at most a constant distance in each step, cannot\r\ncommunicate, are oblivious
and do not have flags or states. The only gathering\r\nalgorithm under this robot
model, with known runtime bounds, needs\r\n$\\mathcal{O}(n^2)$ rounds and works
in the Euclidean plane. The underlying time\r\nmodel for the algorithm is the
fully synchronous $\\mathcal{FSYNC}$ model. On\r\nthe other side, in the case
of the 2-dimensional grid, the only known gathering\r\nalgorithms for the same
time and a similar local model additionally require a\r\nconstant memory, states
and \"flags\" to communicate these states to neighbors in\r\nviewing range. They
gather in time $\\mathcal{O}(n)$.\r\n In this paper we contribute the (to the
best of our knowledge) first\r\ngathering algorithm on the grid that works under
the same simple local model as\r\nthe above mentioned Euclidean plane strategy,
i.e., without memory (oblivious),\r\n\"flags\" and states. We prove its correctness
and an $\\mathcal{O}(n^2)$ time\r\nbound in the fully synchronous $\\mathcal{FSYNC}$
time model. This time bound\r\nmatches the time bound of the best known algorithm
for the Euclidean plane\r\nmentioned above. We say gathering is done if all robots
are located within a\r\n$2\\times 2$ square, because in $\\mathcal{FSYNC}$ such
configurations cannot be\r\nsolved."
author:
- 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: Fischer M, Jung D, Meyer auf der Heide F. Gathering Anonymous, Oblivious Robots
on a Grid. *arXiv:170203400*. 2017.
apa: Fischer, M., Jung, D., & Meyer auf der Heide, F. (2017). Gathering Anonymous,
Oblivious Robots on a Grid. *ArXiv:1702.03400*.
bibtex: '@article{Fischer_Jung_Meyer auf der Heide_2017, title={Gathering Anonymous,
Oblivious Robots on a Grid}, journal={arXiv:1702.03400}, author={Fischer, Matthias
and Jung, Daniel and Meyer auf der Heide, Friedhelm}, year={2017} }'
chicago: Fischer, Matthias, Daniel Jung, and Friedhelm Meyer auf der Heide. “Gathering
Anonymous, Oblivious Robots on a Grid.” *ArXiv:1702.03400*, 2017.
ieee: M. Fischer, D. Jung, and F. Meyer auf der Heide, “Gathering Anonymous, Oblivious
Robots on a Grid,” *arXiv:1702.03400*. 2017.
mla: Fischer, Matthias, et al. “Gathering Anonymous, Oblivious Robots on a Grid.”
*ArXiv:1702.03400*, 2017.
short: M. Fischer, D. Jung, F. Meyer auf der Heide, ArXiv:1702.03400 (2017).
date_created: 2020-08-11T13:48:38Z
date_updated: 2022-01-06T06:53:20Z
department:
- _id: '63'
language:
- iso: eng
publication: arXiv:1702.03400
status: public
title: Gathering Anonymous, Oblivious Robots on a Grid
type: preprint
user_id: '15415'
year: '2017'
...