An optimal algorithm for geodesic mutual visibility on hexagonal grids
<|reference_start|>An optimal algorithm for geodesic mutual visibility on hexagonal grids: For a set of robots (or agents) moving in a graph, two properties are highly desirable: confidentiality (i.e., a message between two agents must not pass through any intermediate agent) and efficiency (i.e., messages are delivered through shortest paths). These properties can be obtained if the \textsc{Geodesic Mutual Visibility} (GMV, for short) problem is solved: oblivious robots move along the edges of the graph, without collisions, to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means there is a shortest path (i.e., a ``geodesic'') between each pair of robots along which no other robots reside. In this work, we optimally solve GMV on finite hexagonal grids $G_k$. This, in turn, requires first solving a graph combinatorial problem, i.e. determining the maximum number of mutually visible vertices in $G_k$.<|reference_end|>
@article{badri2024an,
    title={An optimal algorithm for geodesic mutual visibility on hexagonal grids},
    author={Sahar Badri, Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano},
    journal={arXiv preprint arXiv:2405.13615},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13615},
    primaryClass={cs.DC math.CO}
}