An optimal algorithm for geodesic mutual visibility on hexagonal grids

Autor:	Badri, Sahar, Cicerone, Serafino, Di Fonso, Alessia, Di Stefano, Gabriele
Rok vydání:	2024
Předmět:	Computer Science - Distributed Parallel and Cluster Computing Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	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 $G_k$. Comment: 24 pages, 13 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.13615 Zobrazit plný text záznamu View this record from Arxiv