We propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration (exploration for short) of a grid-shaped network by a team of k asynchronous oblivious robots in the asynchronous non-atomic model, so-called CORDA. In more details, we first consider the ATOM model. We show that it is impossible to explore a grid of at least three nodes with less than three robots. Next, we show that it is impossible to explore a (2, 2)-Grid with less than 4 robots, and a (3, 3)-Grid with less than 5 robots, respectively. The two first results hold for both deterministic and probabilistic settings, while the latter holds only in the deterministic case. ATOM being strictly stronger than CORDA, all these impossibility results also hold in CORDA. Then, we propose deterministic algorithms in CORDA to exhibit the optimal number of robots allowing to explore of a given grid. Our results show that except in two particular cases, 3 robots are necessary and sufficient to deterministically explore a grid of at least three nodes. The optimal number of robots for the two remaining cases is: 4 for the (2, 2)-Grid and 5 for the (3, 3)-Grid, respectively.
The other extreme case is the set of grid-shaped networks REF , where three robots are necessary and sufficient to explore deterministically any grid of at least three nodes (except for the grids of size 2 × 2 and 3 × 3, where four-respectively five-robots are necessary and sufficient).
Optimal grid exploration by asynchronous oblivious robots
ArXiv
ArXiv
Computer Science