Asynchronous Gathering in a Torus [article]

Sayaka Kamei, Anissa Lamani, Fukuhito Ooshita, Sebastien Tixeuil, Koichi Wada
2021 arXiv   pre-print
We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other, but are endowed with visibility sensors that allow them to see the positions of the other robots. Most of the investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configuration. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local
more » ... k multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robots unless it is their current node. As a consequence, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network.
arXiv:2101.05421v1 fatcat:sl6vuaeovfaaffnxrithuischq