An optimal algorithm for geodesic mutual visibility on hexagonal grids
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913367916019712 |
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| author | Badri, Sahar Cicerone, Serafino Di Fonso, Alessia Di Stefano, Gabriele |
| author_facet | Badri, Sahar Cicerone, Serafino Di Fonso, Alessia Di Stefano, Gabriele |
| contents | 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 $G_k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An optimal algorithm for geodesic mutual visibility on hexagonal grids Badri, Sahar Cicerone, Serafino Di Fonso, Alessia Di Stefano, Gabriele Distributed, Parallel, and Cluster Computing Combinatorics 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 $G_k$. |
| title | An optimal algorithm for geodesic mutual visibility on hexagonal grids |
| topic | Distributed, Parallel, and Cluster Computing Combinatorics |
| url | https://arxiv.org/abs/2405.13615 |