Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement

Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case

“…Aljohani and Sharma [16] also showed that COMPLETE VISIBILITY can be solved tolerating, at most, 2 faulty robots under certain assumptions on initial configurations. Recently, Poudel et al [17] assumed a weaker one-axis agreement and presented an algorithm for COMPLETE VISIBILITY in the asynchronous setting that can tolerate any number of faulty robots. An interesting property of their algorithm is that it solves COMPLETE VISIBILITY without arranging (non-faulty) robots on the corners of a convex hull.…”

On the mutual visibility in Cartesian products and triangle-free graphs

“…Moreover, in the context of swarm robotics, mobile robots or agents usually move and operate in a continuous environment (e.g., the Euclidean plane) or in a discrete space (e.g., a graph) [10]. In many cases, it is required to locate (or move) the agents in positions so that they are all in mutual visibility (e.g., see [11,12]). Note that in these works, even if the agents are constrained to move in a grid, the visibility is always checked along line segments.…”

“…Namely, satisfying that for any exchanged information there should be a channel which does not pass through other entities. For some of these applied researches see for instance [1,2,8,15,31].…”

On the mutual visibility in Cartesian products and triangle-free graphs

“…Starting with this initial work, many papers have addressed the same problem (e.g., see [2,4,23]). Later, similar visibility problems were considered in different contexts, where the entities are "fat entities" modeled as disks in the Euclidean plane (e.g., see [24]) or are points on a grid based terrain and their movements are restricted only along grid lines (e.g., see [1]).…”