2023/08/03 by Serafino Cicerone, Cicerone, Serafino, Alessia Di Fonso +5 · 2 citations
Computer Science · #68Q85 #68R10 #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Distributed #F.2.2 #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Search Problems #Parallel #Robotic Path Planning Algorithms #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2308.01855
openalex publication_date 2023/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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 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.