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Computer Science > Distributed, Parallel, and Cluster Computing

arXiv:2308.01855 (cs)
[Submitted on 3 Aug 2023]

Title:Time-optimal geodesic mutual visibility of robots on grids within minimum area

Authors:Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano, Alfredo Navarra
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Abstract:The \textsc{Mutual Visibility} is a well-known problem in the context of mobile robots. For a set of $n$ robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robots are collinear. For robots moving on graphs, we consider the \textsc{Geodesic Mutual Visibility} ($\GMV$) problem. Robots move along the edges of the graph, without collisions, so as to occupy some vertices that guarantee they become pairwise geodesic mutually visible. This means that there is a shortest path (i.e., a "geodesic") between each pair of robots along which no other robots reside. We study this problem in the context of finite and infinite square grids, for robots operating under the standard Look-Compute-Move model. In both scenarios, we provide resolution algorithms along with formal correctness proofs, highlighting the most relevant peculiarities arising within the different contexts, while optimizing the time complexity.
Comments: 28 pages, 9 figures. To appear in the proceedings of the 25th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2023), Institute for Future Technologies, Jersey City, New Jersey, USA, October 2-4, 2023
Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Combinatorics (math.CO)
MSC classes: 68Q85, 68R10
ACM classes: F.2.2
Cite as: arXiv:2308.01855 [cs.DC]
  (or arXiv:2308.01855v1 [cs.DC] for this version)
  https://doi.org/10.48550/arXiv.2308.01855

Submission history

From: Serafino Cicerone [view email]
[v1] Thu, 3 Aug 2023 16:20:36 UTC (1,401 KB)
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