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arXiv · 2405.13615

An optimal algorithm for geodesic mutual visibility on hexagonal grids

Sahar Badri·Serafino Cicerone·Alessia Di Fonso·Gabriele Di Stefano
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Abstract

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 $G_k$.

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Sahar Badri, Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano. 2024-05-22. An optimal algorithm for geodesic mutual visibility on hexagonal grids. https://arxiv.org/abs/2405.13615

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