Complete Visibility for Mobile Agents with Lights Tolerating a Faulty Agent

We consider the distributed setting of N autonomous mobile agents that operate in Look-Compute-Move (LCM) cycles and communicate with other agents using colored lights (the agents with lights model). We study the fundamental COMPLETE VISIBILITY problem of repositioning N agents on a plane so that each agent is visible to all others. We assume obstructed visibility under which an agent cannot see another agent if a third agent is positioned between them on the straight line connecting them. We are interested in fault-tolerant algorithms; all existing algorithms for this problem are not fault-tolerant. We study fault-tolerance with respect to failures on the mobility of agents. Therefore, any algorithm for COMPLETE VISIBILITY is required to provide visibility between all non-faulty agents, independently of the behavior of the faulty ones. We model mobility failures as crash faults in which each faulty agent is allowed to stop its movement at any time and, once the faulty agent stopped moving, that agent will remain stationary indefinitely. In this paper, we present and analyze an algorithm that solves COMPLETE VISIBILITY tolerating one crash-faulty agent in a system of N >= 3 agents.